I'd have to agree. Though not a sure thing, it seems very likely that Alex and John would be related.
Frisco (aka Old Stonewall) is just north of Cochran's on Clear (aka South) Boggy and Colbert Institute which moved from Perryville (formerly Collins' Institute?). I believe Cochran's and the school were on the south side of Clear Boggy. This was on the road from Ft Arbuckle to Ft Smith via Perryville -- often called the Perryville Road or Ft Smith-Perryville Road. This location is in the Chickasaw Nation just west of the Choctaw boundary.
This is the location I think is likely for Camp Kagi (Kahi). I think the Battle on Middle Boggy was about 20 miles northeast on upper Middle (Muddy) Boggy.