A string of coincidences, I'm sure. I actually wasn't able to discover the rock until after I had started the engine and was able to lift the mower, so moving the rock was not the solution to the problem.
While I'm not 100% positive what happened, I'm pretty confident that the real problem was with my starter or solenoid. However, when I hit that rock and the engine stalled, the resulting din sounded like I had done something really, really bad to the tractor. When the starter coincidentally picked that moment not to turn over -- for the first time ever or since -- I jumped to the conclusion that I had indeed done something really, really bad to the tractor.
What I don't get is how sitting in a field overnight fixed my starter. The only thing I can think is that it was hot when I was mowing, and I had been out for a few hours. Right after I stalled a thunderstorm rolled in--on top of everthing else I got soaked walking home. The next morning was quite a bit cooler, and it hasn't been that hot since then. I'm wondering if something in my starting system doesn't like to get too hot.