Family #68 in the 1767 Grimm census.
Family #143 in the 1775 Grimm census.
Family #32 in the 1798 Grimm census.
Family #44 in the 1834 Grimm census.
Birth Record 
Johann Jacob Schott
Baptism Record 
According to the Kulberg Reports, Jacob Schott was a Catholic wheelwright from Mainz, traveling alone under document number 4853, when he immigrated to Russia.  He arrived in Russia on 10 August 1766 on the Russian pink Vologda, a small, flat-bottomed ship with a narrow stern, typically square rigged and used to sail short distances and/or in shallow waters. 
German immigrants to Russia stayed the winter in Oranienbaum before beginning their journey to the Volga River in the Spring of the following year. Shortly after his arrival in Russia, he married Anna Margaretha Becker; shortly after their marriage, she became pregnant. She carried their baby on the very difficult journey east, and both survived. Son Andreas was born just days after the Colony of Grimm was established on 04 July 1767. 
1767 Grimm Census 
By 1775, the couple had another child, Johann Philip, named after his wife's deceased father. His widowed mother-in-law continued to live with the family.
1775 Grimm Census 
By 1798, son Andreas was married and living in another household. Son Johann Philip was married by 1796 and he and his wife had a one-year-old daughter. Jakob and his wife added three more children to their brood: Johannes, Anna Margaretha, and Johann Heinrich.
1798 Grimm Census 
Jakob Schott passed away in 1824 when he was 84 years old. His wife Margaretha is not mentioned in the 1834 census and had probably passed away. Had she survived, she would have been 85 years old that year.
1834 Grimm Census 
This is a complex research project. I'm trying to outline it as carefully as possible. If you have any questions about this profile, please feel free to contact me to discuss.
The Kulberg Reports
There is a Jacob Schott and family listed in the Kulberg Reports, page 131, Document #1796.
This is probably not a complete list of Schotts who immigrated to Russia, as there are several others mentioned in other sources.
The first one, Johann Peter Schott, can be eliminated as a match because clearly his name is different from the Johann Jakob Schott of this profile.
The second one is a possible match.
I checked online resources for German vital records. The only birth record I could find for an Anna Maria Spengler anywhere in Hesse is:
When I expanded the search to all of Germany, there were only a few more possible matches, but most of them were Catholic. Although an inter-faith marriage is always possible, it probably rules them out since this Schott family was Lutheran.
Update: I just discovered the Grimm Schott family was originally Catholic. (See Pleve, Igor. Einwanderung in das Wolgagebiet 1764-1767, Band 2, Heerstellung: Mecke Druck and Verlag, 37115 Duderstandt; Published 1999; page 81.
Miller-33353 12:02, 28 September 2017 (EDT)
If Stumpp's second reference is in fact the Johann Jakob Shott of this profile, then he was married at least twice:
According to Grimm census records, the Johann Jakob Schott of this profile was born around 1740, so that means that Anna Maria Spengler, born in 1729, would have been 11 years older than her husband. That was not unusual during that time in history.
In fact, it's possible that Spengler was married at least once before, making Schott her second husband. She may have had children from a first husband, too, children that Schott took responsibility for after he and Spengler married. This makes sense when you consider that Schott would have been only 16 years old at the time daughter Anna Maria was born in 1756, as detailed in the Kulberg Report. Although that's physically possible, the reality is that she may not have been his biological daughter.
If this Johann Jakob Schott and Anna Maria Spengler were in fact the Schott couple that eventually lived in Grimm, then:
The marriage of Schott and Becker is confirmed using Grimm census records, and the marriage record from Büdingen appears to give proof of Schott and Spengler's marriage.
AHSGR Origins Project
If Spengler and Schott were married before arriving in Russia, their union ended shortly after their arrival. Anna Maria may have died, which is entirely plausible. However, the AHSGR Origins Project suggests that the two may have divorced and remarried, although it's not said in so many words.
First they mention a Schott living in Galka:
The J. Jacob Schott of this record is a match with the other Jakob Schott in the Kulberg Reports. He was a Lutheran farmer from Stolberg traveling under document number 1796.  Traveling with him was wife Anna and children Johann, Anna Maria, and Anna (page 131). 
For those not familiar with the Volga German census records, this means that there are two colonies being discussed above: Galka and Grimm. The bulk of the paragraph appears to refer to a Jakob Schott from Galka, in the 1775 census in family #47. The last sentence, in bold, implies that details about this same man in 1798 can be found in the Grimm census, family #27.
The researcher is trying to say that:
This is wrong, minimally with regard to the Jakob Schott who settled in Grimm. Additionally, if the Johann Jakob Schott from Galka is the Johann Jakob Schott from Stolberg, then the Kulberg record referenced above has nothing to do with the Johann Jakob Schott from Grimm. Here are the reasons.
This brings up another problem regarding Johann Jakob Schott and Anna Maria Spengler. If they were married in Büdingen shortly before immigrating to Russia, what was the status of the children who traveled with them to Russia? They are listed as if they are the couple's biological children. We've already established that the eldest daughter, Anna Maria, probably was not Schott's biological child. Would they have had two biological children out of wedlock? That was not unheard of, but having two children years before they married seems unusual. Were both children Schott's step-children? Or was this a different Jacob and Anna Schott?
More curious is what happened to Anna Maria Spengler Schott after she arrived in the Volga region. It's very possible that she died either on the journey or shortly after her arrival in Grimm. The trip was notoriously perilous and many people died before reaching their final destination. This was not unusual and in fact very probable.
If Spengler's daughter ended up in Galka, however, and her father or step-father lived in Grimm, why didn't she stay with him in Grimm? How did she get to Galka? If Spengler's daughter was born in 1755, she would have been 12 at the time the family arrived in the Volga region of Russia. That was probably too young an age for a girl to go off on her own and live with another family in a village far away from where one's biological father was located. So if in fact she was Spengler's daughter, that seems to imply that her mother, Anna Maria Spengler, was still living and she lived in Galka with her daughter Anna Maria Schott.
If Anna Maria Spengler was still living after 1767, then she and her husband Johann Jakob Schott must have divorced. While divorce was not common among Volga Germans, there are several documented cases of it in the Volga German colonies. If the couple divorced either in Oranienbaum prior to the journey to Grimm or immediately after arriving in Grimm, that would have given Schott enough time to marry Anna Margaretha Becker and allow her to give birth to son Andreas by 1768, the birth year attributed to him in the 1775 census.
If Anna Maria Schott was the daughter of the other Johann Jakob Schott and his wife Anna Catharina, the couple in Galka, then none of this matters. It was a coincidence that she ended up in Grimm in 1798 where the Johann Jakob Schott of this profile was living and they were not related. This makes the comment, see Mai1798:Gm27 very misleading. Only one Schott daughter moved from Galka to Grimm, and she would have been completely unrelated to the Schott family already living there. This Schott daughter was the widow of Christian Zisch of Galka, and one of their children, Johann Dietrich Zisch, lived with his mother and her second husband Gottfried Schultz at the time of the 1798 Grimm census.
The second mention of the Schotts in AHSGR's Origins Project refers to a Jakob Schott, Grimm FSL #68, from Mehlis. It goes on to say:
This appears to reference Anna Maria Spengler, although it does not address the possibility of her being previously married to someone else and of there being any children involved, either from her former husband or her new husband.
I researched the town name of Mehlis and can find nothing but Zella-Mehlis which is currently in Thuringia, although it used to be in Hesse.  That matches what is known about Volga Germans in Hesse being targeted for immigration to Russia, but there is no information about a Johann Jacob Schott being born there. Additional church birth records from that town need to be reviewed.
One of the sources I checked was a collection of German vital records, which kept using the word Schotten along with the surname Schott. Since surnames are often based on a location, I looked Schotten up on a map. It turns out it is town in the middle of Hesse. It seems likely that people with the surname Schott may have been from Schotten or had an ancestor who was at some point from that town. Research on Schotten continues.
Important to note is that both these Johann Jakob Schotts were not from Württemberg, the place we originally thought he was born, although either could have been born there, and then he or his parents could have moved to another town after some time after his birth.
The final mention is both affirming and confusing:
Yes, it confirms that the Grimm Schott was married to a woman named Becker, who clearly isn't Spengler. In fact, The Grimm Johann Jakob Schott was listed as being married to Anna Margaretha Becker in each of the three censuses in the late 1700s. But he could still be the person who married Spengler first in Germany, and Becker second in Russia. In that case, he and Spengler divorced around the same time they arrived in Grimm, or Spengler died prior to 1767 and he remarried.
The confusing part is, KS158 says he was going to Boisroux.  The mention of a completely different village throws a wrench in everything. The only thing that is clear is that whoever was going to Boisroux was a different person, or Schott, from the one in Grimm. Unless this Schott thought he'd go to Boisroux and then changed his mind and went to Grimm. Or he lived in Boisroux for a short period of time and then moved to Grimm.
I looked up the Boisroux 1798 census to see if I could find any Schotts there, and there were none. Interestingly, however, there were several Spenglers listed, and it looks like they were all related to David Spengler, family #Bx51, born in 1740. 
In the 1767 Boisroux census, it says he was a farmer from Dessau.  His wife, Maria, was 26, and they had a son, Christian, age 2. He was of an age where he could have been a younger sibling or nephew of Anna Maria Spengler. Is it a coincidence that his surname is the same as the possible first wife of this Johann Jacob Schott? Are Anna Maria Spengler and David Spengler related?
Research on this family continues.
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