If you look at it in terms of logistics:

There were between 3000 and 5000 male "soldiers", women, children, along with all their horses and livestock and what belongings they had with them. To travel from near what is now Tulsa to west of Yale in one day (which was nearly impossible for cattle drives in the days of cattle drives), it would appear that the Twin Mounds location is out of the question. (yeah...I have heard the arguments in favor, but they do not hold up....in MY opinion).
Then to travel back to north of the Tulsa area by the next day after a running battle....seems unlikely when the majority of your people were on foot.
The Keystone area seems more likely.
However, I was told by Mrs. Gladys Kitchen of the Pawnee County Historical Society that she had seen records she ordered from the National Archives which placed the battle NORTH of what is now Mannford in the far southeast part of what is now Pawnee County. I ahve never gotten back with her to see what she had ordered. I'm more into cemetery recording and locating graves of Civil war veterans, so did not take the time to follow up with her. That is something you may want to do.

For what it's worth!?

Mahlon Erickson
Commander, Dept. of OK SUVCW
Stillwater OK