It is obvious that the drain is plugged up, but I have taken out the freezer bottom cover plate and the freezer back cover plate, exposing the coil fins at the rear of the freezer. I thawed the frozen fins and removed all the ice covering the fins and the bottom of the freezer with a hair dryer, and then applied the hair dryer heat to the drain plug which is located directly underneath the fins, approximately 1 1/2" from the bottom of the fins. However, the heat does not get directly into the drain tube to melt the ice that has formed inside the tube, and I'm reluctant to probe into the drain tube with any type of hard element for fear of rupturing the tube.
How do I get the drain thawed to flush the stoppage out? The only removable panel at the rear of the refrigerator is at the bottom where the drain pan is located.

I had the same problem.. and it SUCKED to fix. Here's how I did it. I took super hot water (not boiling since I didn't want to melt anything) Pour some in the tube... then waited a min or 2. Using a turkey baster I sucked as much as I could back out. Repeated it a LOT of times till finally it melted through.