Several of us have been carrying on a conversation that touches on this Matthew. I agree with you that this Matthew and the Revolutionary War Matthew born in 1757 were probably related. They appear to be about the same age because we know both were old enough to be in the RW and one died in 1841 (TN) and the other was alive in 1838 (GA). Based on some limited data and mostly circumstantial evidence, I have hypothesized that their fathers were brothers.
We are currently looking for an Alexander male descendant willing to take the YDNA test to confirm the hypothesis.
Email me at firstname.lastname@example.org, and I'll share what I have on Matthew (GA) and his probable descendants. I'd also like to add anything you may have to my data base, which I'll share with you.