Solomon, I really think that this is likely to be an impossible task. Bear in mind that the family itself had no record of where they came from. The pedigree given by the family to Hutchins in the 18th C didn't start even as far back as Robert. It's the same in the 16th C when Denis Bond the Ryves neighbour and relation by marriage drew up his pedigree.(uploaded to the Ryves wills page).
It was after the reformation and dissolution of the monasteries that many of these families; certainly in Dorset were able to acquire land. In Blandford, John Swayn, his son in law and the Pitts who intermarried with them are also prime examples of Dorset mercantile families. There were several such families coming from relative obscurity and yeoman backgrounds. (Many did very well for themseves and their descendants, buying up land, marrying to consolidate land holdings and by sending sons into the law and the church.The Pitts (Pitt-Rivers) still hold a lot of land in Dorset.
The Dorset archives don't appear to hold any thing mentioning them before Robert. It is possible that IPMs of Robert and wife Johan(Jane). would give you some more clues. These are available from the National Archives. They will be in latin and it's pot luck on the condition. You can order a digital image of them from the National Archives. You could also order the records you think might be connected to them from the Somerset Archives. (Though it might not get done at the moment since the National and also local archives are closed for the foreseeable future). Obviously there are also several earlier records in the National Archives for people of the same surname but they certainly weren't all related so trawling through these would take weeks of onsite research . You might find some of these earlier records already digitised on http://aalt.law.uh.edu/ . (You need to search first on the Nat Archives and then use the reference to search on Aalt). You might also ask for opinions as to his origins on https://groups.google.com/forum/m/#!forum/soc.genealogy.medieval
I know you feel that the family may have had a French connection and the surname is French in origin. In the records Rive, Reve and Ryve were used interchangeably with Reve used for both IPMs that I can find. It is important to remember that these names are also derived from 'reeve' which is an English occupational surname.
Sorry to be negative. That's probably a personal thing, I'm into their roles in local history rather than pure genealogy. I do think it would be more fruitful to get the later generations right. I thorougly agree that using real primary records is important. We, at least, have far better access to wills and parish registers than Childs, the American author of the much cited secondary source, ever did.
