Today I got the 5.0 boards working properly, even with the current SSRs.

It turns out that adding a snubber across the load doesn't work. The snubber belongs across the switch. I took the snubbers I had added and patched them in across the output side of the SSRs and the problem of the B relay not turning off when the A relay is on went away.

So the boards I have coming this week from OSHPark are going to be "art." I've ordered a 5.0.1 and 5.1.1 version for delivery later this month with the snubber components correctly wired. The difference between the two boards is the 6 pin vs 7 pin SSR pinout. It turns out that the Panasonic SSR with the 7 pin (DIP-8 SMD, but with pin 7 missing) layout is about 25¢ cheaper at Q:25, and if it works, I'll probably go with it in place of the 6 pin part.

UPDATE: I got one of the 5.1 version boards back and put one together for a test. The snubber was wired to the load in this variant, but I used a through-hole resistor to hack the snubber to be across the switch. I also got AQH0223A SSRs to try. These SSRs lack the zero-cross detection circuit, which means they'll be somewhat more robust with an inductive load. That board worked and so that means that the v5.1.1 boards will be the ones to go forward. These are the same, but have the snubber properly connected.