Ice Door Kit, Control Bracket, and Ice Dispenser Guide were purchased. I followed two videos on replacing the parts. The Control Bracket WP2180226 / AP6005965, was straight forward and I discovered a snapped pin on the old bracket causing an electric switch to be out of place... that repair was easy.
When it came to the hinges of the ice chute, I discovered the snap-in, on right side, of the hinge was cracked... this is why the pin escaped. This cracked part is molded into the entire enclosure and was a different-better hinge shown on the video, Ice Door Kit W10823377 / AP5985152.
I used Gel Superglue in the cracked plastic, then JB Weld (15 hr cure) to make a U-shaped thin jacket on the hinge. After curing, I mounted the door flap, this time with a custom shaped very thin metal washer at the right side/outside which superglue was applied to the top two edges of the snap-in hinge to hold the washer, bridging the gap above the pin and strengthening the part similar to the fully enclosed pin in the videos.
The new flap is working, the new flap return dampener (basically a plastic piston) seems a bit restrictive and takes quite a while for the flap to seal the ice chute.
The ice and water dispensers are working again. Noticeably less pressure is needed to actuate the ice or water. Overall, a good repair with a bit of Mcgivering. If the crack had completely snapped the right side of the hinge, it would require replacing the entire enclosure, which doesn't seem to be a part available through your website.