Switching wires on the board as well as unplugging the wires on the board is a good idea to be 100% sure that the issue is in the controller, wished I'd thought of it sooner. There is no pattern to the calls latching; the car could be idle, running up or down, top or bottom of the hoistway, with or without passengers etc. The reason I didn't go after the traveler yet is because even if the call signal goes to ground, three other buttons (in the correct sequence) would also have to ground.

By the way, I did call MCE and they were not full of ideas. They suggested checking for power supply issues (mainline to mainline) and looking for sources of induced voltage.