They would have known from previous trips and assessments of the Round Earth lat/lon readings how much fuel they would need to bring for xxx Round Earth miles.

If you travel 300 miles on a road trip, according to your GPS, and your tank is half empty you have an idea on how much fuel you need.

If people can get "an idea" on how much fuel they need for x Round Earth miles, that means there is a set amount of fuel (within a margin of error, of course) a given vehicle needs for a certain amount of RE miles. You also seem to assume they can extrapolate from the amount of fuel they need for x RE miles to the amount of fuel needed for, say, 3*x RE miles (i.e. three times the amount). All this leads to the assumption that, while a RE mile may not the same distance as a "real" mile, it still describes a constant distance and therefore is proportional to a "real" mile (i.e. there is a constant c such that x RE miles are c*x "real" miles).

Under this assumption, the approach presented by 3DGeek still works.