Have you contacted the Chattanooga Natl. Cemetery to check their records as to when the date of interment was? Were the
soldier's remains removed from the Chickamauga battlefield; or perhaps the site of a field hospital elsewhere?
I'd also contact the historian @ the Chickamauga battlefield to see if they might have burial records. Were the dead from the
59th Ohio, or the brigade it belonged to, primarily buried at a specific location? Was the soldier ID'd as "JMF" among them?
I think its a good chance that "JMF" is your ancestor, but at this point in time, we'll probably never know with certainty. I doubt
they'd entertain the thought of digging him up, and comparing DNA.
Best of luck with your research !
Greg C. White