Between all the noises that were bothering me, and how alarmed J was at the noises when she heard them, and the fact it was well off warranty, we decided to get a new hot water tank. It was installed on Friday evening.
So, now the tank no longer makes ticking, thumping, and booming sounds when it’s heating, and check this out:
There’s a nice, big, deep drip tray with a hose outlet that goes right to the drain. So even if the tank starts to leak, the water will collect in the tray and run down the drain. There’s still always a chance that the tank could fail at a seam, but even then the outer shell should contain it and direct it into the pan. If the pan overflows, it’s right near the drain anyway.
I think this is a good thing, and should at the very least move the tank much lower on the list of things that bother me. Considering how much it cost to get a new tank installed (holy crap!!!), I hope so.