Take a Q-tip and some rubbing alcohol and clean that up first, then follow the traces back to the first via you come to, then prep and use that via with a small jumper wire and 'rebuild' the trace. That's far from the worst that I've seen and can be fixed for sure.
There are scans on the forums here of the different controller versions also, so you can see where the traces originally were. I can't say the repair will go smoothly, as prepping and soldering to a via is a bit harder than an existing solder joint, but take it slow and keep your soldering iron tip clean and tinned. Being 'too hot' really has about jack all to do with it, besides shorting the life of the tip, it's the time you're keeping it on the solder joint that lets the pads get so hot they delaminate from the board.
