Well, after some more staring and head scratching over the caliper, something occurred to me. But I thought no at first....
Well, then when it came time to try to push the piston back in just to see... well it was a no go... it wouldn't push in... open the bleeder valve, still no go... remove it entirely and put it on the bench, still no go with a C-clamp.
Turns out that what occurred to me did turn out to be the truth. Recall that the pads were not only wearing uneven with each other, but also on an angle on each pad itself. As the pads started to wear down further and the piston started to extend further, what happened was... Due to the angular wear of the pads, the piston got 'cocked' and after it extended out so far, this caused the piston to jam. Therefore the piston was able to continue to extend out for braking, but could not retract back properly, nor could it be squeezed back.
In the end, what it took was taking a brass tap rod and hammer and tapping it on the one side. Then the piston went right in like nobodies business... So I was able to re-use it and did so for reasons I'll explain in a bit.
The opposite side did not have the same issues, but did have equal angular pad wear.
In the end, I just replaced the pads with Bendix pads and called it a day.
The reason is my plan. The plan is that I will monitor pad wear over time on the original equipment to rule out the previous pads as the blame.
If I see angular wear on the new pads start to develop, then I will have to start hunting down the source of the problem.
But, I do plan to totally replace everything with new stuff at the next pad service. New calipers, rotors and pads. I just didn't want to possibly hide some other problem by going all-new now.