I can't really offer much advice on how to fix the damage to the tires, as shaving or fixing out-of-round tires is not something I've ever had any experience with. However, I will offer this:
What happened to you here highlights perfectly the biggest reason why I will not trust ANY electronic supplemental braking system. Potential is always there for it to malfunction and over-brake your toad. And, in many cases, by the time you realize its happening, major damage has already been done to either your tires and/or your toad brakes.
Once you resolve the tire issue, my suggestion is that you dump that braking system you have and get you a
Readybrake. Simple, very cost effective cable operated braking system, that is just about impossible for it to ever over-brake your toad (once installed and set up properly).