Not exactly sure how far the harness runs but you are exactly right that with the original thinner wiring the problem will happen again. If I were splicing in new I would splice it either to remove as much of the lighter gauge wiring as possible or at the simplest point to access it when it happens again. I also suggest replacing the blower motor as well, the reason for failure is an overload condition which is caused by a large load from the fan not spinning easily enough. The larger wiring is simply a bandaid to be able to take a larger current flow ...but the resistor pack still can't take it.
Think Outside !- No Box Required.