Things at LAS should be slowing down after the holidays, but I would say you should plan for having no more than 4 hours on/near the southern end of the Strip (as others said already.) Grab a taxi for the trip to/from the Strip. I don't think you want to do a car rental as all dropoffs are at the remote, centralized ground transportation center - indoor garage, after refilling the tank ? plus then a 5 minutes walk down to street level & wait for next available shuttle for a 10 minutes ride back to the main terminal - less time to "enjoy" Sin City itself with your layover.

LAS security started getting busy very, very early in the predawn hours - and UA/CO's flights are few & in-between, and the line to get pass security can be rather long - plus, you will need to take the shuttle train out to the satellite terminal for UA + then walking upstairs to find your gate. We used to do lot more UA into LAS, and it's easily 20 to 30 minutes from wheels on the runaway to the taxiway, docked & into the terminal, walk & ride to the main terminal & downstairs/bypassing the luggage claims and then out to ground transportation.

I say if everything worked smoothly, you will be on the Strip no earlier than 1:15 or 1:30 am and need to start getting back no later than 4:00 or 4:15 am with your carry-ons and SSSS on the BP so as to allow extra time to wait in line & clear TSA. If you have UA/CO status and/or flying F or J, there are priority lanes and will save you a few minutes.