The 3rd IHG did do much scouting and fighting guerrillas in SW MO until the Indian Brigade moved into the Cherokee Nation in early 1863 where it generally remained the rest of the war. It did find itself fighting some of the same men when protecting supply trains on the military road from Ft Scott KS to Ft Gibson in the Cherokee Nation.

I'm not sure about the "whites" in the 2nd IHG. I don't know if they were white citizens of one of the Indian Nations or whites dodging conscription by trying to hide in the Indian Territory. I agree it would be odd for the times to have white recruits under Indian officers in the US army. There were many whites under Indian officers in the Confederate Cherokee regiments in Indian Territory.

The land of the so-called Five Civilized Tribes - Cherokee, Chickasaw, Choctaw, Muscogee (Creek), and Seminole -- was held in common by the tribe prior to Oklahoma statehood (1907). The US Government imposed an allotment process whereby all the land was allotted to tribal citizens. There were likely many veterans from both sides who received allotments in this process. My grandmother's allotment was on the Missouri line just north of Southwest City. She sold it and moved to Muskogee where she had family. My cousin Lucy lived on her allotment her entire life, from 1904 until her death in 2004.