I have also always driven in/out. We leave the strip around 5 and hit minimal traffic. We also stay until the end every morning and it's an absolute shitshow lol. The only thing I can say is to try your best to park as close as possible to the exit, which makes for a farther walk but makes your exit way faster. Another pro-tip is to keep a cooler in your car (even a cheap Styrofoam one works fine) and have it stocked with some cold drinks/fruit to make your wait bearable. We usually get back to the strip around 8 AM.

Getting dropped off early might not be too bad, but I would never ask anyone to try and pick me up through that mess in the morning.