We've camped at 9400 ft in western Wyoming with more than one rig over the years - never had a problem with LP.
The only issue was the pressure accumulator for the water - we live at 165 ft above sea level, and I adjusted the tank when I installed it. However, at camp, the pump pulsed like it did before the installation. I thought about it for about a half second and realized the accumulator was already expanded... I never did adjust it for that elevation as we only spent a week there.
I suppose some bright bulb will come up with the bright idea that he needs to adjust the pressures in his tires at those altitudes...
Enjoy your trip!