MCRider, Flybox, BJbuchanan, Mtnmotors et al...I finally got around to trying on the old shoes, which still had plenty of pad left but are 40 years old, and it all works like it's supposed to. The EBCs were not uniformly thick, causing the spongy braking and, somehow, making it so the more I tightened the rear axle, the harder it was to turn the wheel.
The old brakes were contaminated with a little bit of grease, but my friend said a little sanding and cleaning with rubbing alchohol would take care of it. It brakes strong now, so I'm satisfied if no one thinks the contamination issue is a problem.
Thank you all for your help!