Yes, I agree the draining puzzles me. It only happens when the failure to start occurs, and I let it sit for a while. Once the battery is recharged it starts with no problem. This tells me that something gets reset after the battery discharges.
You are describing a stuck/hung up relay. I'm not saying for CERTAIN that is it, but still...
(I spent 30 years in component-level troubleshooting - I'd almost lay money on a sticking relay on the RCM and that would explain everything. But, of course, I do not KNOW for sure.)