I have nothing specific to help, sorry.However, itis very possible that your Mary Converse descended from Deacon Edward Converse of Woburn, Massachusetts who arrived in the US in 1630.His descendants are well documented... but, as I mentioned, I could not find your Mary.I looked at just about every Mary I could find in the two volume set:The Converse Family and Allied Families by Charles Allen Converse 1905.
My own Converses went from Mass to CT, to Vermont, to NY and finally Michigan.Many went west similarly and ended up in Ohio.Jefferson County NY is mentioned in the books for example, p 117 Thomas Converse born in Mas removed to Woodville, Jefferson County, NY.Lucy Converse born 15 Nov 1774 resided in Houndsfield, Jefferson County, NH.Rodman is another town mentioned.
Perhaps the marriage records for that town in Ohio will give you the next lead... or death records in Michigan.Most states started keeping records of births and deaths in 1867.
Sorry I can't find your Mary... but she will turn up.If only our ancestors had written more of all this down!!!