Hmm sounds like a muscle motility (movement) issue then. Why would our muscles not move as they should to evacuate stool?
1.) You say it's not inflammation as you can retain stool, remove that plausible cause.
2.) Second plausible is non-inflammation rectal wall thickening. If you had an xray, your rectal walls would appear thickened, it looks like a lead-pipe in xrays, so it's called lead-pipe. It can be from scar tissue formation. When our rectum walls are normally thin, the muscles within move in patterns of motion that move stool along. When the walls are thick, that results in either diarrhea (rapid, muscle spasms) or constipation (incomplete muscle motions).
You could try a fleet enema to move things along. You said the stool was right there but just wouldn't come out on its own.https://radiopaedia.org/articles/lead-pipe-sign-colon