I have thought about doing much the same thing (as an experiment to see how practical it is), and had decided in my own mind that I would try to claim money back as a 'mileage expense' through the normal channels. My employer only asks to see a petrol receipt for a mileage claim to be re-imbursed. On very long trips, a mileage claim might just approach the cost of the avgas...
I can't see that this goes against the spirit of our PPL.