I've got a GE over the range model and have spent the last two and a half hours trying to solve the same problem. I just fixed my microwave in about ten minutes once I saw the light.
Open the door and work from the inside. There is an inner seal that sets in from the outside of the frame about a inch or so. This has tabs that makes it attach to the metal frame. Put a putty knife between the seams and loosen the tabs.There is a video on YOUTube that shows how this is done.
On my GE this lets you see another screw that allows you to remove the handle.

Next, there is a faceplate with the holes that the handle fits into. This faceplate will pry out if you pry towards the outside edge of the door. Once this is off you have to apply the putty knife to the seam between the outside frame and the inner metal frame that holds the glass. )I discovered this with my thumbnail !)
The trick is finding that line between the aggression that breaks something and the timidity that solves nothing--just keep gently trying different angles for prying the putty knife.

Congrats--I figured I probably saved about the same!