The damaged tracks shown connect to vias which route the signal between different layers on the board. Most signals are on top/bottom layers, +5V and ground are mostly on the internal two layers.
As opposed to just scratching at the corroded tracks, you need to check continuity then repair tracks and vias if they're open circuit. I wrote this guide which may help. It's for the A4000, but the A3000 PCB is much the same - it's still 4 layers.
Use something less damaging than whatever you're using now. A fibreglass brush works well, e.g. Radio Spares part no. 514-868
Looking at your images, the U400 and U450 sockets are probably corroded as well and will need replaced.
Perhaps there's an option to pack up the MB and send it to a professional. Perhaps not to Antarctica though.
