The modern engine does much better at managing the fuel-to-air-mixture, the turbo-charged/supercharged engines don't generally have this problem at higher elevations (watch a Pike's Peak race
)
When I would take the CJ or Healy to much higher elevations it was a PIA to keep them running smooth, my brother-in-law's dad (mechanic) taught me how to adjust the carburetors for reasonable fuel-to-air-mixture and not have them die but they would get slower and slower as the elevation increased and engine HP decreased.
Pretty sure the rule of losing about 3% of the HP for every 1000’ above sea level still holds true even for today's engines, I run ethanol free gas or premium when driving in the mountains to avoid knocking but likely a carryover habit from carburetor days; It may be placebo affect but I think premium/ethanol free gas helps the HP levels.
As for gas mileage, in my experience, with the loss of power so goes the mpg at higher elevations, only time I've noticed it slightly increase is using ethanol free gas or going downhill.
My personal experience with tire pressure, as I get higher in elevation, tire pressure decreases. When I leave Tx, my tires are set at 35psi and by the time I get to Utah destination, they are usually around 30-31 so it works out for local driving around. If I take the Durango route, I usually have to add some air, the ARB under the hood has gotten a lot of non-trail use
Over the years, I've been told running lower octane at higher elevations is better, not something I have tried but will be doing so on the next fill-up, IF I remember after a couple of tanks of 85 octane, I'll post up my thoughts of this test.
Last note, filling up the inside of your Jeep with gas does not help it float and make it lighter while driving, it only pisses off your passengers and the dog...
