Well, I overcame my paranoia about opening them up. The repairs were straightforward but tedious. I first extracted the crossover and noted that the mechanical connection between the two large capacitors and one of the smaller ones had failed in the drop. I was able to hot-glue the small one, which I believe was the original construction technique, but there was not enough room to do this with the large ones short of desoldering and removing them, so they are now nestled in a bed of flexible silicone sealer.
All of the connecting tabs on the crossover needed to be straightened out, and one of the connectors to the tweeter had come off the wire and remained on the tab. This was recrimped and soldered (didn't have any silver, unfortunately).
Next, I removed the batting from the cabinet to extract the mounting hardware (two screws and two washers) that was not loose at the bottom. At this point, it was time to open up the good speaker (and the point about working with MDF is well taken--I already did not want to be repeatedly removing these screws) to see how things were supposed to be mounted. Oddly, or so it seemed to me, the washers go in between the crossover and the cabinet. With the batting back in place, this proved to be a surprisingly different task to accomplish, as the washers really seemed to want to run and hide in it. After something like two hours, I finally hit on snipping a bobby pin in two and using the halves as a guide.
The lower screw would not bite, so I wound up using a slightly fatter one and a drop of carpenter's glue. I waited for the vinegar fumes to clear up, reassembled the two, and (zippo-bang) was off to the races--irritate the neighbors at 4 in the morning with some Leadbelly to see if the balance was even. All seems to be well, although the 1978-ish amp that I have from middle-school days in Arkansas might not be the best standard for testing!