–Finally fixed the sprinklers for good: when I replaced the anti-siphon valve I neglected to connect the white common wire to the four solenoid common wires. Duh. All god now. Except:
–Grace heard water running into the pool, so I turned the spigot off, hard, and broke it. Turned off the water main and looked at it; it’s completely indecipherable to me, with at least three rubber gaskets where one would do. Discovered fairly quickly on the web that it’s not a pool-specific thing, but rather another irrigation anti-siphon valve–manually-controlled in this case, not solenoid. Pretty sure SiteOne will have what I need to repair it, early tomorrow after a trip to Noah’s. Meanwhile, the house water is off.