If you keep hunting in history focused on people vs places you sometimes figure something out. Following up on Pike's conference at Tahlequah and the players involved led me to this article by Cheatham.

https://www.kshs.org/publicat/history/2003autumn_cheatham.pdf

There is a synopsis of John Allen Mathews role and how the interplay between Mathews, Dorn, and the Jesuits impacted the Osage and SE Kansas. There is a map on pg 175 that overlays the CONFEDERATE protectorate boundaries that make the actions of Mathews much clearer. I believe Mathews was looking to remove pro Union settlers from the northern strip of land in the Osage Reserve that had been excluded in the confederate treaty protectorate not the historical federal treaty lands. This would have been a strip across Allen and Woodson Counties if I read the map right, in the historical Osage Reserve but not in the CSA treaty area perhaps due to the 4 non-signatory clans led by Hard Rope which would have been in the area.

To help with modern maps:
Osage Mission = St Paul KS
Mathews Post = Oswego KS
Humboldt and Ft Scott KS have kept their names.
Mathews was killed at Chetopa which was in the Quapaw Strip along the KS IT border.

An 1860 map of area of concern is here:
https://mapgeeks.org/kansas/#!fancybox/c9a531a2/1860-Map-of-Kansas-and-Missouri.jpg
Note the lack of survey/township lines in the area of the Osage Reserve and Cherokee neutral area. Historic place names are ledgible. White Hair's Village or Great Osage Village is where Mathews trading post was located now known as Oswego. Boudinot was a failing protestant mission.

JJR