So I gained relatively accessible access to the pipe break, applied the pipe repair clamp, stood on my head in the dirt and rat droppings to get both hands in (one for the wrench, one for the screwdriver), and finally flipped the switch!
The result: the pipe clamp isn't tight enough, and still drips, and now I can hear another jetting break under the floor in the other back room. So I'm not quite there.
But at least I don't have to disassemble the entire house brick by brick. And I can see some light at the end of the tunnel. Or actually, light shining through into the basement from the crawlspace -- but it's the same principle.
Update: here's the pipe repair clamp in situ: