Elmer or anyone else for that matter,
My thoughts and questions, off the top of my head...
Did Phillips march from Ft Gibson to North Fork Town? I thought he marched west from Ft Gibson to Hillabee and then sent a detachment to North Fork Town to leave corn for the other battalion of the 14th KS Cav. It is my understanding that they didn't have corn or much of anything else at Ft Gibson -- one of the reasons for the expedition. They got corn from the region west of the Texas Road and then carried it back to North Fork Town. Did some or part of the expedition actually follow the Texas Road from Ft Gibson via Honey Springs to North Fork Town?
Colbert's Mill was presumably near Reagan where the fish hatchery is located. However, Danny Knight, a descendant of Gov. Winchester Colbert, places his residence on the Boggy near Frisco (Old Stonewall) and near where it is believed Robert L. Cochran lived -- where the Ft Smith-Ft Arbuckle Road crosses the Boggy (aka South Boggy or Clear Boggy).
This all fits rather well. If Phillips was right about the location of the battle -- on Middle Boggy in the Choctaw Nation -- and that is the location of Camp Kansas, then the South Boggy is about 20 miles south and would make a reasonable location for Camp Kagi (or Kahi -- I presume these two are the same) and allows for Phillips to have easily visited Gov. Colbert's home.
Phillips (Willetts) could then have pushed south and burned Colbert's Mill. I don't think they went to the Chickasaw Rock Academy because it was not destroyed. They apparently came within 20-30 miles of Ft Washita and Boggy Depot.
This would have been down Leavenworth's Trail, which I believe is called the Dragoon's Trail, from Leavenworth's expedition in the 1830s. The Choctaw-Chickasaw border roughly followed this route and I believe this was the road from Ft Holmes to Ft Washita.
I think it is significant that none of the reports of expedition (Union or Confederate) mention any of the landmarks on the Texas Road or movement on the Texas Road. There is no mention of moving north or south on the Texas Road and no mention of Perryville, Geary's Station, Little Boggy (aka North Boggy), Alex McKinney's, Davis' Crossing, or Mrs. Flacks'. There is no reference to being near to Ft McCulloch or Armstrong Academy. And as you reiterated, Phillips post-action report, written to show he was successful in accomplishing everything he set out to do, said that he would invade the Choctaw Nation later -- this time he only invaded the Creek, Seminole, and Chickasaw Nations.