John, A couple of things to wrestle with....
I don't think the academy further north (near Shawnee Town)is the "Rock Academy". The Chronicles article on Old Stonewall mentions the Rock Academy out of context and the author apparently has this confused with what he called the Chickasaw Academy located just across the Boggy from present Frisco. It was Wapanucka Academy (Rock Academy) for which there were special provisions in the negotiations for the Chickasaw to separate from the Choctaw, not the academy near Frisco.
The northern one, on the Ft Smith-Ft Arbuckle Road, is shown as Cochran's Academy on some old maps. However, I can't find squat about it. Since the Cochrans lived on the Boggy across from Frisco, per the Chronicles, I've assumed Cochran's Academy is mis-located on the old maps but this is pure speculation.
That reference to ___ ____ Courthouse drives me nuts! I have tried to find a researcher who can find the original handwritten reports of the ORs to try and figure out what the transcriber couldn't read. My theory is if it said "Boggy Depot" the transcriber could have figured that out so I'm guessing it either said Chata Tamaha (Choctaw City -- Armstrong Academy) or Tishimingo, the Chickasaw captial. Tishimingo fits my theories better and makes more sense for Jumper to go from there to Ft Arbuckle. On the other hand, per my theory, Jumper could have been anywhere from up near Shawnee Town to near Frisco and the courthouse could be some Chickasaw district courthouse we don't know about. I've also pondered if it was "Boggy Depot" and the reference to Ft Arbuckle should say Ft Washita... though I think Jumper wasn't at Washita and his location was unknown by his superiors (They would have known if he was at or passed through Ft Washita.).
Your thoughts??? ... and anyone else please join in!