By now you have found out setting all to A1 results in all AMs turning OFF as soon as the first MS times out. CORRECT!
There can not be a sequencing problem if appliance modules are parallel not series. How are you wiring the outputs in parallel? Extension cord with two plugs?
A single lamp with 2 bare wires, a short wire plugged into each AM, the white commons and the black 120V wires are wire nutted together with the 2 lamp wires.
I believe that isolating the outputs via relays (as suggested) may be the only solution.
I believe that the solenoid valve may operate on DC, if that is any help.
Strange, stranger, strangest.
With AM#1 set to A! and with AM#2 set to A3, if I hold my finger on each module and press either MS-16A sensor OFF button, I feel a click in each AM?
?
It seems that the parallel output is allowing the OFF signal to go to both modules.
?