And even when you throw H20 into the mix, it only comes into play if there is enough moisture that it changes state
I don't think so.
Per Dalton's law, the total pressure for moist air is the sum of (dry air partial pressure) + (water vapor partial pressure)
The individual partial pressures can be calculated from the gas law in molar form:
pV = (m/M) R T
where m is the mass and M is the molecular weight and R is the ideal gas constant.
In other words, the rise or fall of the partial pressure relates to the
inverse of the gas molecular weight. Or, equivalently,
proportional to R/M, which is the specific gas constant.
Water vapor has a molecular weight of 18.02 g/mol. Dry air = 28.96 g/mol.
Water vapor's specific gas constant is 461.5 J/(Kg K), dry air = 287 J/(Kg K).
So we can see, given the same rise or fall in temperature, the water vapor partial pressure will change (461.5/287) =
1.6 times faster than the partial pressure of air.
Typical "dry air" sources available track side still has a lot of moisture in it.
Oh, and unlike aircraft tires which are inflated to around 200 psi, we typically ran around one bar pressure - in which case whatever was inside the tire prior to beading was a significant percentage of the total.
For racing applications, the air in the tires are typically removed (towards but above vacuum) before nitrogen is added, to achieve better than 95% Nitrogen, same as in aviation.