aggieemt, OK, I guess ... We can wait and see at this point ???

Aggieemt, Yes, it's possible for a fill valve to have a slow reacting solenoid or diaphragm. First check to make sure the water filter isn't dirty and has been replaced recently. Then check to make sure the refrigerator is level, then check to make sure the ice maker is level(in both directions) inside the freezer compartment. If all's OK, then replace the fill valve.

Aggieemt, Yes, the [Part number: AP5263471

Agggieemt, To return the fill valve, you can contact the AppliancePartsPros.com Customer Service Team (1-877-477-7278) They will be happy to assist you in the return policy and procedure. You can also enter the AppliancePartsPros.com web site, enter the parts order screen, and scroll to the bottom of the page. Under the "Customer Service" heading you'll see "returns". Click on the heading, the system will advance to the cancellation and return policy screen, click on the return header ( light colored box) and follow the instructions.
What to do next ? Check and find out what other circuits, components and machinery are attached to the same GFI outlet, You may want to get a GFI outlet with a higher rated amp rating. Replace the GFI outlet with a "standard" 120 VAC/60 Hz., grounded and polarized outlet. If codes require you to have a GFI outlet, Replace the outlet with a higher rated outlet and make sure the circuit is a "dedicated" circuit for the refrigerator only.

Aggieemt, Don' know where to take you from here. Other than an amp check with a clamp on ammeter. That could eliminate the refrigerator as the problem. Turn on or plug the refrigerator into the outlet, wait a few minutes, place the ammeter claw around one of the wires to the compressor, you should read approx. 1 to 2 amps, once the system equalizes. The test start the ice maker. When the arm reaches the 2 o'clock position the heater energizes and draws 1 to 1.5 amps, the amps will drop when the arm reaches the 7 o'clock position and the cubes start to rotate up and out of the mold. When the arm reaches the 11 to 12 o'clock position the fill valve should energize and draw less than one(1) amp. So you're highest amp draw should be less than a total of 5 amps. Most GFI outlets are rated at 14 amps or less, which is one of the reasons why they aren't recommended for a refrigerator circuit . " Being that it only trips a GFI, and it doesn't trip the breaker when the fridge is plugged into a regular outlet " also indicates the problem is the outlet or circuit, not the refrigerator.