I got home, bailed the old toilet with bucket and sponge until it was "dry enough," pulled it out and chucked it on the lawn (I'm so white trash). Then came the prep work of cleaning off the old wax seal, getting the new one in place, setting the bolts, applying the plumber's putty and seating the new toilet in place. It took a bit of work to get everything lined up but eventually I got the basin seated. My only real complaint at that point was that the anchor bolts that came with the new toilet are so long that they're holding the caps off the toilet's base. Better too long than too short, though, so I'll keep my complaining to a minimum. I made quick work of getting the water tank attached and then plumbed in the supply line. It was time to take the toilet for a a test flush!
The good news was the new toilet flushed pretty well and it looked like the wax seal seated just fine. The bad news was there was water pooling on the tile, so I had a leak somewhere, probably up near the tank. I did some exploring and discovered that the leak was not the seal between tank and basin, it was the water supply line! Water was dripping from where it attached to the tank as well as where it was attached to the shut-off valve. A bit of poking didn't yield any result and so I called it quits at 2030 to give lady_curmudgeon her Valentine's Day gifts. I was going to need a new line, preferably one that wasn't so long that it would kinked up as badly as this one had gotten, and I didn't feel like going out for Yet More Parts last night.
This morning, after a bit of frustration while playing "guess the size of the nut," I managed to take the old supply line off the toilet and the valve so I could do some proper measuring. The old line was vinyl, 12" in length and around 11/16" in diameter. I needed something that was more like 8" in length so it wouldn't have to bend and twist. I made a quick trip over to Lowes and found a 9" supply line in braided stainless steel for around $4. While I was there I also figured out what size the nut was (16mm... what the hell! Fits a 3/8" outer diameter pipe thread and is metric?!). Bought the hose, came back home, found my adjustable wrench and set to putting the new line in. 9" is a bit longer than the 8" I really need so I had to do a bit of bending on the line, but it went in relatively easy. Tightened down the valve nut, tightened down the tank nut and turned the valve on. Shortly after I took it for a test flush and ... everything worked. With no leaks this time. Hooray!
So that's the conclusion of the gust toilet replacement saga. If I had to guess I would say the crack that necessitated the replacement of the toilet began when I tried to put a new flush handle on the old toilet... and then I had a leaking supply line when I put the new toilet in... etc etc.
Let this be a lesson in home ownership: Never touch anything.