While I don't want to say that everything is super peachy, I want to recognize the positive direction the GreenHouse plumbing problems have taken.
After the previous plumber left (without figuring out or fixing the problem and charging me $160), we tore out the pad and carpet from Josh's closet and mopped up the water in the adjoining utility room. A puddle formed again way too quickly, and I figured it looked like it was coming from the hot water heater. Then I remembered that our realtor paid for a home warranty, and I called the warranty company to place a service order. This morning, a plumber came over, said, "Oh, yeah, it's definitely your water heater" and replaced it before 10:00 am.
After he was done, I asked him if he thought this should have been a hard problem to diagnose. He said that it could have been diagnosed in 10 minutes.
Guess I know which plumber I'll call again. (The GOOD plumber, by the way is Clinton Thomas Plumbing, in case you live in UT and need a plumber.)