The scheme would require some kind of massive, centralised planning to be enforceable. Charging individuals differing amounts for fuel is the first error, in my opinion. Also assuming that anyone queueing up at a fuel station has 'insider information' - what if all stations in an area are out of petrol? Does that criminalise every person queuing?

It seems you're presenting this idea in the context of some kind of future American society. Instead of working to socialise fuel, I would hope that by 'then', we would have moved away from ICE passenger vehicles.

I also wonder if you're trying to solve the problem from an oil-producer's perspective, or government perspective - basically capitalistic or socialist approaches to the situation.
Checking fuel guages, VIN etc. would all require extra personnel - why not just get some armed guards/police to secure fuel stations, and allow them to sell available supplies for whatever price 'the market' reaches 'equillibrium' at?
Price spikes + extra security seems to solve the issue for me.
If American neighbourhoods devolve into armed confrontations, you only have your military-industrial complex to blame.

Or, simply ration fuel - weren't 'they' already doing that for truckers somewhere?