No joke, you're nuts for trying to UV max this. Especially given that monsters can roam around and end up in places you've already cleared. Good luck on regaining your sanity.
6 hrs and 8 mins making left turns only. You still end up exploring most of the map, but you get all three keys and then the exit so less backtracking.
8hrs in and I have found the exit and all three keys. Likely 3 more hrs of backtracking now. I made only right turns until I found the last key and now only left to find my way to the exit. Next is seeing if only left turns are faster and lets me get all three keys before the exit (I found the exit before any keys).