Thanks. I successfully replaced the house battery, and I don't think I damaged anything. I had more trouble with the corroded battery holder than I did with the solar electronics.
After I disconnected the negative terminal, I connected an ammeter from the positive terminal to the frame, and it showed a current of about 1.25 amps. Then, I thought of the chassis battery, so I disconnected the negative terminal of the chassis battery. The current from the positive terminal of the house battery to the frame was then about 1.5 amps. If the batteries are properly isolated, shouldn't I measure the same current, regardless of whether the chassis battery is connected?
I then pulled the fuse to the solar controller, and the current went down to zero. Then I replaced the battery.