With enough bodge wires, any PCB problems can be overcome. It's difficult to tell from the pictures if the transformer is repairable or not, that's the kicker. I'd imagine you'd have to get one from another parts unit, and then you may be better off fixing that one.
I dug a clock radio out of the trash can at university about 22 years ago - someone must have thrown it. The transformer was ripped off the board and damaged. I was able to epoxy the transformer together and solder paper clips to the windings to make new leads. I can't believe I was able to repair it, but it worked for 20 years after that. I left it at my parents home and my mom got tired of looking at it (it was missing knobs, was badly scratched, etc) so she threw it away.