Well, here I am again, a week later, still with no water but with the beginnings of a major improvement.
To catch y'all up, last week after the first plumber and I parted ways when he said he doesn't take payments I got a second bid from another plumber who does take payments.
Public Service Announcement: don't open a sealed bid whilst driving, talking on the phone (Bluetooth), eating chocolate biscuits and drinking tea because once you see that the first digit of the bid is a 5 and there are three more digits after that before the decimal point, you will swallow half a biscuit, say very bad words your nearly 90-year-old mother shouldn't hear, spill your tea, and almost drive off the road.
Nothing says "I think I can come up with a pile of cash after all" like getting a second bid that's more than double the first one. After I pay for this plumbing, I'll be broker than the Ten Commandments but at least I won't be deeper in debt.
The first plumber came back on Tuesday to look again at the situation and map out a plan. There are the usual difficulties you'd expect with an old house, but the biggest problem is that most of the plumbing runs under a concrete floor in a crawlspace about 14 inches high. There's no practical way to access that crawlspace--"you could lift up the whole house and have a new foundation poured with a full basement", he said, and then we laughed and laughed--so he's going to abandon that labyrinth of galvanized pipes and figure out a different route for the new plumbing.
Wednesday morning the plumber showed up bright and early and by the end of the day he had the new water heater mostly in and one bathroom plumbed. Thursday he'll be back, with another plumber to help him, and if all goes well I should have water by nightfall. Fingers crossed.