Why do propellers have less theoretical range (i.e. range ignoring impatient passengers wanting to go fast) than jets, despite greater efficiency?
For more background, this question is about the usage of Breguet Range Equation (I find this explanation better suited for this question)

There are many problems with your calculation:


Time unit of speed should be the same as the time unit of SFC. For your first calculation, since you used mph for speed and lb/(hp*h) for SFC, your SFC term shouldn't have 1/3600. For your second calculation, since your speed is fps and your SFC is also in lb/(lbf*s), there's no need to have 1/3600 either.
For both calculations, end result should be the same unit of length. Your first calculation uses mph and the second uses fps, so the the end result would be in miles and feet so not comparable. But since you made the mistake #1 you end with numbers still on the same order of magnitude. 
For the propeller case you are using PSFC (Power specific fuel consumption) rather than TSFC (Thrust-specific fuel consumption). Breguet Range Equation requires TSFC to work.




If you look at the Breguet Range Equation you see the only difference between prop case and jet case is TSFC. So to compare relative range differences, you only need to compare TSFC and avoid all other complications.

Take Cruise TSFC from some modern examples:


GE90: 0.545 lb/lbf/h
Europrop TP400: 0.38 lb/lbf/h


(1/0.38)/(1/0.545) - 1 = 43% so with everything else being the same, prop should have about 40% more range than jet.