Maybe you could try lowering the water temperature. Axolotls tend to heal faster at a lower temperature. Try putting him in a small tub and putting him in the fridge. MAKE SURE THAT THE TEMPERATURE DOES NOT GO BELLOW 5 DEGREES CELSIUS THOUGH!! put an empty tub in the fridge and leave a thermometer in it, or check it once it has fully cooled down, to check the temperature before you put him in the fridge.
don't put him in the already cooled tub, that was just to check the temperature. When you put him in just put the room temperature tub in, so that he cools down with the water.
Also, keep a separate empty tub in beside your Axolotl so that you can place him in it, changing his water every day without changing the temperature.
I'd do some research about putting axolotls in the fridge before you do it so that you are prepared for anything.