I got a rod (aluminum) locally. I flushed twice with vinegar, and half a dozen times with (a few gallons of) water. The first flush was rustly. After that, all I got out was lumps of that white chalky stuff. Eventually, it ran clean. Then, I connected everything, and started it up. It doesn’t seem to be leaking (4 whole days so far), and the water is clear.
Thanks for your help.