I'm pretty sure that the use of N2 in aviation tires involves entirely different reasons.
6500 feet of elevation difference should be worth about 3 psig.
9" is the minimum recommended rim width for that tire size, which is generally designed around a 9.5" wide rim. Assuming that it's the tire size you want, the wheels really are a little on the narrow side. That, and some tires more than others, can make for greater sensitivity to inflation pressures.
It is entirely possible for a solid axle to have cambers or toes that are not zero. Be careful about making "obvious assumptions". My other stick axle car actually has about -0.5° rear wheel camber (as well as nearly as much toe-in). No, I did not modify it to make it that way (I would never have put the toe-in like that).
Nitrogen still has to obey the gas laws. The only difference is that it comes out of the fill station with less moisture content than what your average regular air source gives you. That affects pressure rise during operation, meaning that the pressure in the N2-filled tire will rise somewhat less. But an N2-filled tire will still show a temperature-caused increase in pressure with driving.
There is some evidence that N2 diffuses through the tire carcass at a slower rate than O2 and most of the other trace gases. But a good "tight" tire shouldn't leak much regular air out, so this is not as big a benefit as the N2 equipment outfits would have you believe.
Hope they didn't charge you anything extra for the N2 fill.
Norm