Just thought I'd bump this thread since I decided to take this route to cool my tower lines.
Here is the top of the tower. Copper goes almost all the way to the top and then I used polyethylene insulation (1-1/4" I think) to go around the tubes. It runs the length of the tower and then stops since we want the bottom part to be exposed to the cold air and absorb and transfer the temp.
Here it is through the bottom. Mine goes quite a bit further into the fridge than the OP since this was the pre-cut length they sold (2') and it seems fine (will transfer better probably).
Final view of inside the fridge:
Total cost was $10 even for two 2', 1/2"-diameter copper tubes and a 6' length of the insulation.
I just rigged it up so I'll have to report later on effectiveness but I think it will work well.