Russell, I’d suggest calling GE back. Doing any repairs yourself could void your warranty. I would request a different technician to come out to diagnose the issue. If you aren’t shutting the door completely, your freezer wouldn’t be freezing properly either. Most people will notice the door open because that refrigerator has an alarm that beeps. I’m not buying what the technician told you. Especially if you’ve been making sure the door is closed.
The issue your experiencing is typical for a defrost problem, gasket issue or a fan motor. Either way, it is all under warranty and you should not have to pay for repairs
You have an expensive, top of the line refrigerator and your warranty is to protect you from costly repairs. The right technician will be able to solve the problem. Unfortunately, not all technicians are the same. Request a different technician or even request the lead tech. People do it all the time. Use your warranty while you can.