I suspect someone knows why Monique went back to the hotel. I think that she would call someone like her mother or sister and talk about what was so upsetting that she left the game.
It doesn't make sense to me to leave his phone at a hospital cot room but exit himself where he was surely picked up by footage having him leave and return. Surely, the footage is kept long enough for police to go through it. Perhaps, it is as you say, he figured that he wouldn't be that much of a suspect.
Another thing that just amazes me is that he left casings behind. I don't care if I have to scour beneath the bed, I'm going to find all of the casings for the gun. Also, why on earth would you keep the gun, the silencer and the fake license plates?
None of it makes sense to me unless this guy had been stealing drugs somehow from the hospital and was hooked on drugs. That's the only way that I can see someone who is supposedly successful screwing up his life this much.
If this goes to trial, we might also discover if any notices went to MM and MT by error concerning their divorce. I myself think that it was caught in time (like the next day) for any notice to be mailed. Now, if the court had their emails, notices may have been sent to those in error. In fact, if this is the case, maybe, that's how the error was discovered, by either MM or MT calling in and alerting them to the error.
All speculation on my part.