Selectively measuring AC magnetic fields with a Hall sensor (and getting an accurate Tesla reading)
This answer is purely theoretical.

I see no additional problems with measuring a slowly varying magnetic field with Hall sensor - the output voltage will be a slowly varying signal.

However, due to Hall effect being a capacitance effect, there is intrinsic low pass filtering nature to a Hall sensor. It should not be an issue in at the frequencies of interest to you, but worth watching for in higher frequencies applications.

The accuracy of Hall sensor at low frequencies should be approximately the same as at constant field. Check the specs.

Inductor alternative:

I don't think that using an inductor is a good approach. Hall sensors are small and accurate, whereas inductors tend to be large and messy. The inductor has an intrinsic DC filtering capability, but this is not a major advantage. 

If you can find a sensor based on induction which fits your application - go for it. However, I suggest you don't try to build one yourself (maybe for fun and education, but not for real applications) - it will certainly be worse than almost any hall sensor you can buy for a few bucks.