So today I replaced the toilet valve; wife was at ballet so I could turn the water off for a bit if I needed to.
ProTip: when installing a valve, make sure said valve is in the "off" position before turning the water back on... The ferrule was sitting the the compression sleeve a little cockeyed, which was the equivalent of holding your thumb over the end of a garden hose.
I sucked up all the "loose" water with a shop vac, then worked it with towels, and now it's air drying with a fan. It'll be a couple of days before I can push forward again.