how do you measure the coil in the crossover?

Go out and buy a DMM with inductance and capacitance capability. You can get them for less than $100 new and will get a very handy piece of equipment to have around anyway. Be sure you disconnect at least one lead of whatever you propose to measure.

you need to measure not only the inductance value but also the Q factor of the choke, which a simple DMM won't measure. An impedance bridge is required but that's simply cost prohibitive. You'll probably need to find an electronics lab to check it out.

The Q isn't going to vary that much if you stay at around the same DC resistance, which the DMM should be able to measure as well. It's certainly going to be more than close enough for any cheap speaker.

My other comment is that replacing the capacitors (use Solen/Chateauroux at the very least) is going to make an even bigger difference than the inductors.