One area you might want to look at is the CSAR assets (PJ, HH-60G, HC-130). They've been bounced around quite a bit over the past couple of decades. Recently, they were briefly part of AFSOC but were place back under ACC after less than two years IIRC. The reason, so I was told, was two-fold:

First there was controversy over adding additional roles to CSAR assets. In essence, AFSOC wanted them to do more than just CSAR. ACC did not want the CSAR mission diluted. That is putting it very simplistically.

Secondly, the program to replace the HH-60's which was deemed too big for AFSOC to handle given its other responsibilities at the time. I heard that the intention was to put CSAR back under AFSOC once the helo fleet was recapitalized, but of course that program isn't going so well (to put it mildly), so who knows at this point.

Anyway, take all that with a grain of salt as it's what I heard from others a couple of years ago, but it's an angle that might we worth exploring in your research.