There are some military reasons that Phillips and Blunt did not advance to the Red River. In the Perryville Campaign, Blunt could have driven Steele from Middle Boggy (near Atoka) and gone on to Boggy Depot, Ft Washita, Armstrong Academy, etc. but the further south he moved, the more he had to worry about Arkansas on his left flank and the unknown size and capability of the enemy there. So, he has a good excuse for pulling back from Perryville and sending Cloud toward Ft Smith and the 2nd Colorado west toward the Little River. Phillips had a similar problem on his expedition. He didn't know his enemy's condition and his flanks became more and more at risk the closer he got to the Red River.
Back to the issue of keeping the Indians as enemies... You may note that Chief John Ross received a rather cool reception in Washington (where Ross was never liked or trusted anyway) and after the war, the US Govt wanted to negotiate with the Southern Cherokee, not the Loyal Cherokee. There were two Cherokee delegations in Washington at the same time and the govt preferred dealing with the Southern Cherokee 'businessmen' over the idealistic and isolationist Loyalists.
Regarding Albert Pike... I've always felt sorry for him. He was such an idealist and tried so hard but he just couldn't seem to grasp the big picture. He fell into such dispair after Pea Ridge that he was nearly useless to 'the cause'. He kept waiting to be better armed and supplied and was so upset that the Trans-Mississippi had been abandoned but he couldn't grasp that the victorious Northern Army of Pea Ridge had gone east of the Mississippi as well. He had little opposition and he had Watie operating alone in the Cherokee Nation. Chief John Ross and Drew's Regt turning over can be blamed on Pike. Had Pike and Cooper been along the Arkansas and Canadian Rivers and followed orders from Hindman, the Locust Grove debacle would not have happened. Pike was afraid of being caught like a 'rat in a trap' so he nearly abandoned the whole Indian Territory.
I don't know what happened to the "Indian money". You know that most of the Indian trust funds were invested in Southern banks -- a good reason for the Indians to side with the Confederacy. I have considered the Confederacy virtually bankrupt from the beginning of the war -- their only hope was a negotiated peace before their credit ran out completely. The devaluation of Confederate currency eventually made the trust funds worthless.
You'll remember that Confederates could not pay the Indians prior to Pea Ridge (March 1862). The war and the treaties were less than a year old. The Cherokee Treaty was less than six months old! Yes, Pike used some of his own funds and credit and what he did buy would get confiscated by others. For the first year of the war, it was true that it was more practical to supply white troops than the Indian troops -- the white troops were much more effective and easier to train and discipline. However, it was soon a waste of resources to supply disaffected whites instead of the Indians.