I got my best information going to Butler Co and examining the records in person (and a graveyard). There was also a lot of original early Ohio (Cinci settlement) documents at the Newberry Library in Chicago (like Columbia's general store A/R list circa 1791). If I saw anything related to Matthew I would have written it down. I think your Matthew may have been Jeremiah's nephew based on his date of birth. It may be impossible to put the pieces together definitively due to the amount of time that has passed and lack of records in that area.

If I find anything, I'll let you know and will post it here, but I haven't been actively researching for about 10 years now.