Ken this is an interesting mystery to say the least. I think there are better clues yet to be had. I'm in the process of firing up my ESRI GIS system to see if I can do some map overlays and then plot known locations against time.
A number of locations in this area are introduced in the OR not in association with this battle, but with other unit movements. For example Cochran's Academy was considered the front door to the Chickasaw Nation in one report. The road from Fort Gibson to Old Fort Arbuckle in another with way points. Clearly not the Texas Road.
Phillips own description leads me to believe he was north of the Canadian River for a good portion of the time particularly the several days "cleanning out the Little River Area"
I'll keep digging...