okay, all the below is probably wrong, but fwiw....
short answer is I think the 60Hz lug -> common lug wire length is shorter (the 60Hz lug is connected partway along the length of the winding).
it's not really a resistance thing tho, it has to do with the rotating magnetic field/flux being generated in the stator and how the rotor responds to it. Probably best to google how a shaded pole induction motor works...it may help to look up "squirrel cage rotor" as well.
the equation is:
E - sinusoidal (A/C) voltage
f - frequency
N - number of turns of wire around the stator
M - Maximum flux density the stator can handle ... it's a property of the metal and the way it's constructed
if ya assume the voltage is constant at 120V and the desired flux density is constant, then a decrease in frequency needs an increase in turns of wire to keep the equation balanced.
if you don't have a multiple tap winding, when you lower the frequency you must be increasing the flux toward the saturation point and the current will increase ... along with the heat. Compound that with the fan spinning at a lower rpm and you've got a problem if the motor wasn't designed for it.
so if you have a 50Hz connection, use it. It'll reduce the heat. Your Hawaii motor should have cooked faster on the 60Hz tap. The reason the thing fried to begin with is usually the shaft components are cruddy and the torque required to turn them goes up. There's more formulas, but as you'd expect more torque = more power = more current = more heat.
I suppose if you don't want to get a good explanation elsewhere, you may be wondering how current snuck into all this since it's not obviously in the formula above. It's hidden in the M term. Flux is generated when a current flows through a wire....or when flux is present, current is generated in a wire. It's kinda the linkage between electricity and magnetism.
so who wants to measure the resistance of the motor winding and shoot all that down? You could also just look and see if the 60Hz lug has a double winding wire on it (it's in the middle of a daisy-chain) and the other two have just a single wire.