After review, I cannot say for certain that a failed "Engine Control Relay" output on the RCM would NOT look like this.
I've never had the "mystery no start" due to such a failure.

I still hate to see you buy a new RCM. I'd really like to see you reflow the joints on the board, or get someone to do it for you. And since you said moving stuff in there got it going......... I'm moving to the position of "maybe it IS the RCM's EGR output...."