First, permeation decreases with pressure, at different rates for the two gases. If you consider only this fact you will find that the partial pressures of O2 and N2 asymptotically approach homeostasis, rather than simply all the O2 leaving and all the N2 remaining.
Second, permeability changes with temperature, so the ratio of O2 and N2 exfiltration rate changes seasonally, as each gas has a different permeability-vs-temperature curve. Third, the ideal gas law causes pressure changes seasonally which will also decrease exfiltration in winter, and once again, each gas will have its own permeability-vs-pressure curve, so these become very confounding factors.
All in all, the reality of the situation is that filling up your tires with atmospheric air will probably settle on partial pressure ratios of, say, 85/15 rather than 100/0. The deflation that you get comes from only about 5% of the O2 leaving the tire; and of course you get another big deflation when the weather first turns cold.
I don't know the exact numbers because I've frankly never thought to look into this before. So like I said, it was a clever thought! But it needed to be taken a few steps further.