Okay, good news and bad news, I think. I got everything put back together a few days ago. Filled the system with clean water and then went home for the day. When I got back the next morning, there was some water on the concrete under the tractor, but I think it might've been from a little overzealous radiator filling on my part. I dried it up and went back home.
It was a couple of days before I got back out there, but there didn't seem to be any new moisture on the concrete. Good sign, I guess. Anyhow, I put the radiator tester thing on and pumped it up to about 15 psi. The system mostly held the pressure, but after a few minutes, there was a steady drip. It looks like it was coming from a little hole on the front right side of the water pump (see photo; the little hole in question is directly above the bolt head on the hose clamp smack in the middle of the image).
I crammed a rag down in there to catch that drip, dried the concrete, and waited. A little while later (maybe 20 minutes? lost track of time working on the boat) there was a whole new drip. I cannot see where it's coming from, but it appears to be the underside of the water pump (see photo; this is not a very useful image, but I can't get a shot of where the water is coming from. It appears to be coming from back up under where the hose is attached, somewhere on the body of the pump).
I'm hoping these leaks are indications of a bad gasket or something similar. My birthday is next week; karma could give me a nice present by making this a quick, cheap fix.