"July is the 7th month of the year."
No Frank, it was not. You need to read that page more closely. While the Romans may have used January as the first month of the year, the Western Christian world had been using March 25 as New Years Day since the 12th century at least. This is what Old Style vs New Style dating and double dating is all about.
It is fundamentally important to understand the difference between the Julian and the Gregorian calendars, or really Old Style vs New Style dating. While the Gregorian calendar was instituted by Pope Gregory in 1582, the British Empire did not officially adopt it until 1752. The English were very much aware of the different calendars and a mix of dating styles can be found in the records. Old Style dating was used almost exclusively in early records (say 1582 to1650) and New Style dating became more common later (say 1650 to 1750). Don't hold me to precise dates it varies wildly according to place and time.
These months when written as "7 mo 6 day 1641" is Old Style dating with the first month of the new year beginning on March 25, and the 7th month therefore being September.
This is a Genealogy Dating Page I started but haven't quite completed.