MKR GPS Shield library only works if you call GPS.Available() non-stop

Nope, it will only run on a MKR apparently.

There are several GPS libraries that have been around for a few years, so it might be better to use them since there is a fair number of people experienced in thier use.

There are probably very few people around with knowledge of that particular MKR GPS Shield library, so you might need to rely on support direct from Arduino.