Yikes! A bit of a mess with the rewiring and the damaged tracks as a whole... likely you could have a number of vias/pads/tracks and such that need further scrutiny - not to mention those under chips...
One fellow I know contracted an 'assembler' to clean up and rewire his board... might be the most practical option if you don't feel you have the technical/hands-on skills.
Old Crow talks about removing those damaged traces since they're infused with the battery substance and can continue to decay/leach into good areas. From IMG_2913, the area I was mentioning is the 4051 stamped IC's, likely nested in the area of the ceramic capacitors standing closer to halfway across the board - opposite the battery. Your board could be an earlier rev so just look for the one with the stamped part number 4051 - should be two of them.
Otherwise, if the board is still in the original condition you really need to remove those damaged sections and replace with suitably sized wires... for fine stuff use wire wrap wire.
The induction of noise from stray wires is also a relevant issue....