Just to follow up with some sort of closure, it turns out I had a few problems.
Number 1, my clutch linkage was a little worn.
A representative sample:
On top of that, I hadn't adjusted it properly. Until I really got under there with a flashlight, I didn't realize just how much pedal free play you get from a little extra space at the throwout bearing.
It turns out, however, that those weren't the real problems. The real problem was that I'd run out of spline on my input shaft, so the clutch disk ended up pinned to the flywheel.
I just installed a washer on each bolt between the transmission and bellhousing. Problem solved.