Some of your research needs to be in the direction of Montgomery County, Indiana.
Especially the U.S. Federal Census year of 1830.
In Montgomery County during the 1830 census the enumerator took these
names:
Alexander Montgomery,2-2-3-0-0-1 males.
Alexr Montgomery, 0-1-0-1-0-0-0-0-0-0-1 males.
This last Alexander Montgomery was aged 80-90 years.
{meaning he was born between 1740 and 1750}
I think if a map is used, that Montgomery county adjoins Parke County?
Supposition says that he may have died between 1830 and 1834, as in
about 1834 John Montgomery went to Peoria County.