Can't remove twist-style / turn-style / knob cap on overflow drain in tub
(Answering my own question.) After trying a million things, I went with the destructive option. I used a metal file to shave a hole into the knob so I could access the screws on the plate behind it. I unscrewed the screws, turning the knob to be able to access each screw, and then took the whole assembly out. Afterwards, I soaked the still-fused-together knob and plate in CLR for 10 hours, and by the end, it still didn't come apart. After looking closer, it might be the case that the knob was held in place by a screw on the opposite side of the plate, which, when mounted to the tub, is completely inaccessible unless you open up the wall behind the tub and cut into the overflow waste pipe. What genius designed this?