without going too much into details I don´t think it is impossible to prepare a set of wheels with variable volume to keep the pressure in the wheel constant so as to eliminate those effects.
Of course you can take the easy way first and use (illegal)tyrebleeds to achieve a halfway house (I think in Rallying Michelin had something called a leaking tyre valve to achieve this)you set the optimum inflated pressure and as long as the temps rise you will remain in optimum inflated shape..unfortunatelly a safety car phase will kill you if you have no magic 4 drops of H20 available to release into the tyre to regain pressure...So yes it is possible to get there even on very limited recources.
I´m aware this is not going to be legal to use in a race weekend ,but with some thought you could even find a legal solution to the task.
which brings me to the point that you´d need different pressures for different tasks (low pressure for ultimate traction ,high pressure for high speed high downforce points on the track )to get the whole thing really working for you. I guess If someone picked that up and made it work he could gain quite a bit over a lap and a race...
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