There's a difference between a shorted element and one with a leak to ground. It is very possible that the element is good other than a leak to ground. The fact that it did not blow the fuse on the board, but did trip 2 different GFCIs indicates that's the problem. You further proved the problem to be the new element by reinstalling the old one and verifying the fault was gone.
A ground fault is not necessarily a short. It is usually a small amount of power leaking to ground. Your GFCI is designed to detect this type of leak and shut off the circuit if one is present.
GFCIs are not circuit protectors, they are people protectors. When someone is getting shocked, their body basically becomes a leak to ground and that's what the GFCI is designed to protect against. An element with a leak to ground will also cause a GFCI to trip. It's usually caused by an internal winding touching the metallic casing, or moisture trapped inside the element. If not for the GFCI, you most likely would never know there was a problem and the element would work just fine. I see this sometimes on RVs that have been stored, but then put back into service. In many cases the problem can be solved by powering up the refer via an extension cord plugged into a non-GFCI outlet. Usually an hr or so of running in this fashion is enough to burn off moisture and clear the GFCI problem.
But since this is a new element, I wouldn't mess around with it. I'd exchange it for a new one. A ground fault is reason enough to replace an element because even if you are successful in clearing the problem, it will most likely come back again. Tim
