I talked about this inverter on my Youtube channel (routercnc). One of the early episodes in the drill press conversion series. If I understand what you need to do I think a latching relay arrangement would do it? The output contacts would control the run/stop X4, but other contacts on the output side would cut power to the coil itself so it wouldn’t start again until you armed it. There might be better ways but this was my first thought on it.