A few comments off the top of my head...
Opothleyahola's band did not move from the vicinity of Skiatook in one large caravan. Many bands scatterred taking various paths on their trek north and begin moving before the battle of Chustenalah. The authorities in Kansas didn't want them in the midst of the white settlements so they told them to go west. They were told to look to Black Beaver's Trail which is persumably what was later known as Chisolm trail to near Wichita KS. The Cox Map shows a group heading across Osage County toward the mouth of Walnut River (Ark City) but shows other routes as well. After Chustenalah, Watie pursued a group straight north about 20 miles which would be the vicinity of Bartlesville, on the assumption they skirted the Osage Hills on the east. Cooper pursued a group across the Osage (i.e. Osage County). Due to the distance and the weather, it seems they would want to head more north than northwest. The descriptions of them in Kansas by the Indian Office say they were scatterred over a large area when they first arrived.
When I can make some time, I'll review what sources I have and will post again.
Ken