I think the reason for the western route was primarily to forage. Phillips couldn't keep his troops, the refugees, and his horses fed at Ft Gibson. I think the clearing of the "Southern Indians" or getting them to "turn over" was for the same end. I think the armies had consumed or destroyed any substenance along the Arkansas River and the Texas Road which is why the Creeks had moved southwest and the northern Choctaw Nation was virtually abandoned. By this time, Honey Springs Depot, North Fork Town, and Perryville were abandoned or destroyed so he had to take a western route to forage along the way.
That report from Little River Town (Rivertown?) with the reference to "OLD" Ft Arbuckle is quite odd. Little River Town suggests the town was along the Little River. Old Ft Arbuckle is, of course, on the Canadian River and not near Little River. It seems unlikely but not impossible that Phillips in person was as far west as Old Ft Arbuckle. I have speculated that he or the transcriber erred and it should read "Old Fort Holmes" with Little River Town nearby.