Final followup on this one:
Assumed to be fuel starvation due to something blocking the tank pickup. Once it began to start again, it has done so consistently and reliably, and it has run with no stumbles and plenty of power.
My best guess matches what someone else suggested upthread: that because of the low fuel level and the severe incline of the car, a big piece of rust or other crud in the tank managed to occlude the outflow.
I thought that my refilling the tank partway and vigorously agitating the car by jumping on the bumper would knock loose any debris. Perhaps it did, in retrospect -- the car didn't start instantly after I did that, but I only cranked it for thirty seconds or so. It did start the next morning.