One thing to keep in mind is that propane is stored in liquid form, and requires heat to vaporize. Vaporization draws heat from the surrounding area and if the buried tank isn't big enough relative to the gas draw, the tank will 'freeze up' and you'll be stuck with no gas pressure.
I had to use a vaporizer (essentially a 'water heater' type unit) on my 10,000 gallon tank on the farm to alleviate the low gas pressure problem.
The fuel rate demand for a normal generator is low and where I live the ground is warm (I’m in central CA).
Interesting problem though...