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?

I believe rationing by price is always more effective than rationing by quantity, and is much easier to administer to boot.  But I see no reason why we couldn't easily setup a two-tier pricing system that would benefit relocalization forces in detritus use, limit the worst of Jeavons' Paradox, yet still respond overall to the international price of crude/barrel.  Scanning the barcode VIN # is much better than the odd-even day rationing we had back in the earlier days and all the corruption it created.

For example, my little scooter combined with my lack of owning a cellphone puts me at a decided disadvantage in moving to the 'early bird' front of the gasoline queue.  A pickup owner, with a cellphone for inside info, and extra gas cans in the back of his pickup can beat me to the forming queue every time.  My attempts at Powerdown are working against me, even if I can afford the 4 gallons to fill my tank, if when I finally reach the gas pump--none is available. Yet, long-term, I want the price to go as high as possible, so others will be forced to eventually downscale in their vehicle use too.  

Trust me: I had the gas siphoned out of my '69 GMC pickup in the early seventies--It was no fun waiting 24 hours till my even-day came up, then waiting in a hours-long queue in the blazing sun with a five gallon gas can to later heft a quarter mile home for the partial refilling of my tank.

Riding a scooter vs. driving my old pickup effectively triples my energy circle's radius; I can cover a much larger territory, if needed, for the same cost.  But, by staying within the original radii or less; by trying to relocalize myself as much as possible, it creates big savings for me and the environment.  With the two-tier system, I could buy 1/4 gallon outside my neighborhood, pay the distance penalty cost, yet know that I have adequate fuel so that when I get back to my neighborhood, that I can refill near my house at the going market rate.

Rationing by price as a function of your distance from home is how nature imposes it controls--I am merely proposing the same for us humans.  A predator cannot seek prey further than it's abilities to bring the bacon home to feed Momma and the kids; it's energy level constrains it to patrolling a discrete territory-- as detritus energy becomes limited, I suggest we must all learn to travel in increasingly smaller circles.

Bob Shaw in Phx,Az  Are Humans Smarter than Yeast?