NoWhammies

After just under 40,000km my cycling shoes have developed holes where the back of my achilles tendon hits the shoe. I suspect I have some funny movement in my foot b/c my running shoes all wear out in pretty much the same location. As this is the only part that is wearing out on my shoes, I am look for suggestions on how to repair my shoes. I went to my tailor who is jack of all trades. She suggested just putting duct tape on there. Not a terrible idea, but I am worried that a) the rubbing of my foot - which has caused the hole in the first place - will just rub on the tape causing the tape to slide sideways leaving b) a gummy and gooey residue. Especially during the heat when combined with sweat.

Any suggestions? Here is what the problem is. Thank you.