[NB no Sr or Jr really, but one has to distinguish between the Matthews] I have all of Matthew Sr's sons except Alexander dying in Indiana. I have Matthew Jr, 1781-1855 in the Monroe Co, VA census in 1810 and the Washington Co, IN census in 1820.
Phyllis Lenart is my source for them moving to Indiana in 1815 or 16, but I don't think she told me why she thought that. She had him serving as a private in Capt Andrew Nickell's Co of Infantry, 4th Regiment, VA Militia during the War of 1812. So that narrows it down to 1812-1820.
Out of curiosity, what is your source for Matthew (1781-1855) having middle name Harvey or initial H? I've certainly seen that as the middle name for his son on some land grants, but the only docs I have for this Matthew are census, and no middle name.