Replacing the element is really trivial. You can test it by measuring resistance between a lead and the case- you should get zero ohms. A bad one will measure in the millions of ohms or lower. It may well work fine after running on LP for a while- the elements get a bit of moisture inside, which gives a very high resistance path to ground- enough to trip the gfi. When they heat up with the LP, the moisture can be driven out.
I've replaced hundreds of elements, and never had an issue breaking anything, other than a 30 year old Dometic that I had to break out the old element and install a new, smaller one wrapped in a brass shim. Worked fine for several more years.
