You are right about the detachment of cavalry being at North Town and I think the Infantry took the more direct route to Hillabee. I think Hillabee was North of the Canadian.
Because of the infantry and wagons moving so much slower, Phillips kept detaching the cavalry.
Here is the clincher. From Camp Kahi, Phillips decides to trim the force down to 450 mounted men and one cannon. Phillips says he sent the Infantry and wagons "back" to Little River. From Camp Kahi he sends out two more mounted detachments of 40 or 50 each to make a demonstration to where he thinks the enemy is located and to try to entice them to attack Phillips main force at Camp Kahi because it is a good spot to defend. The detachments probably went toward Ft. Washita and Boggy Depot.
Feb. 15 Phillips report comes from Little River Town near Ft. Arbuckle.
I think because of the Infantry Phillips did not take the route through Perryville, to Boggy Depot.
I don't know all the details but I think we are getting the route roughed in.