At risk of repeating myself, I'll summarize the journey again: When I first dry-fitted mine, the pads wouldn't go into the gap. I felt around in there and found that there was a burr on the top edge of the abutment plate that was stopping the pad from going into the gap, so I took a file and in 10 seconds or so the burr was gone. The pads still wouldn't go in, so I filed the burr off the edge of the pad backing plate. Then, it went in until it hit the "bump" and stopped again. Getting it past the bump required a hammer.
I pulled the bump-equipped abutment plates (at the bottom of the pad pocket away from the bleed screws - all it takes is a Torx T25 hex bit) and flattening the bump with a hammer and anvil. They were still tight, but the pads would go in without jamming. After two days at a race track, the pads now slip in and out just fine - you'd never know that they were ever too tight.