Yup, use zep as a first pass for cleaning, rinse thoroughly, then desolder the affected parts, sand the affected traces (removing the mask from any affected copper), use zep again to clean off the remaining alkaline, rinse thoroughly, blow dry with an air compressor, then air dry, then repopulate the board, and seal exposed traces with nail polish.

You can't really trust anything on that board diagnostically without addressing the corrosion.

Just go to the PCB diagram and parts list and order what you need. Most suppliers I'm aware of have gotten away from doing kits.

GPE's site is handy since the listings for the kits are still there, so often times, you can use those to help find the individual components.

Give it more than a day. It's a one man show.

Yes, that's a really good sign, and it's a worthwhile board to repair. Corroded boards that give no indication of life generally take a bit more time and effort since there's usually a few more issues than just the corrosion.