The the headwaters of Boggy River (aka Clear Boggy or South Boggy) and of Middle Boggy (aka Muddy Boggy) are in the Chickasaw Nation far northwest of the Atoka/Stringtown area.
Cochran's was on the Boggy River on the road from Perryville to Ft Arbuckle, just south of Frisco/Old Stonewall. This vicinity better fits the ORs as the location of Camp Kagi/Kahi. Twenty-one miles northeast of this point on the upper Middle (Muddy) Boggy and its tributaries, along the Chickasaw-Choctaw Boundary, fits the ORs as the location of the Battle on Middle Boggy.
I'm still looking for credible evidence that contradicts the Official Reports of Phillips and others.