Progress! The pool has been refilled and–amazingly!–the pump still works!!!! Whoever designed this pump with whatever fail-safe or idiot switch to shut it down when it's starved for water has just risen to my Circle of Awesomeness. Gauge pressure is correct, water pressure at return is correct, no funny noises, no unusual vibrations.

The water stayed clean because I added bleach throughout this ordeal and mixed it in manually. The bottom is a little dirty but that should clear up soon, now that I can filter again. The cave-in is truly ugly, what can I say? We'll live with it.