Problem solved. The first time I used the hair dryer I reached in and thawed the exposed tube. I thought I had it all thawed, but when I reinstalled the water line in the rear of the fridge, water still leaked out of the back.
Two weeks later, after much thought, I removed the ice maker and discovered there was a block of ice in the far back of the fridge, beyond the tube. With the ice maker removed I was able to to reach the back section, and thawed it and the tube. This time, using a syringe, I actually tested that water could flow from the back of the fridge through the tube. Then I put it back together. Now water leaked out the front ice dispenser! ugh.
A week later and after more thought I removed the ice maker and discovered there was also a block of ice in the ice maker itself, where the water exits the tube. This was causing the water to come out of the tube, bounce out of the ice maker, and flow down into the ice bin, draining through the ice dispenser opening in the front door. I thawed this block of ice in the ice maker, and put it back together.
Finally, after 30 minutes, and with all of the ice melted (finally), it began to work perfectly. No leaks.