I didn't read your post properly, and nearly replied:
'Why don't you use another relay triggered by the second system's power on state (power light or something) hooked up to the 12V rail that supplies the invertor...'
But no, you're there already. I don't see any problem with that, it would just be like having a redundant light switch in your lounge-room to save you having to walk across the room in the dark to turn the light on.... If you wanted to be a little tricky you could just use the one relay and seperate the trigger from the Opus and the trigger from the second system with some diodes. Might work. Might not, who knows?