Cut it out and replace it.
Desoldering corroded parts of the board are tough, as you know if you've ever worked with corroded boards.
Traditional desoldering methods just don't work real well. Cutting components out, and heating 1 leg at a time from the solder side of the board and carefully pulling through the component side has the best success rate for me.
PIAs aren't tough to come by. Yeah, they aren't cheap, but there are LOTS and LOTS of pulls out there. Look up Andrew, he has plenty of good clean Motorola pulls.
https://pinside.com/pinball/forum/topic/fs-6821-pia-mc6821p-starting-at-3-each-legit-no-remarks-tested
Having said that, I've got concerns on that board being salvageable. It's got a lot of creep on it from the corrosion working around. All the spots where there are black dots in the traces (look, for example, above U51), that means the solder mask needs to be removed from the board, and sanded clean down to bare copper traces, which then need to be tinned or otherwise sealed. Otherwise, it'll continue to spread under the solder mask, and eventually, will eat through those fine traces on the component side of the board.
Any board is salvageable, but not every board is *economically* salvageable.
I would also suggest removing the lamp matrix column resistors and transistors, and convert to mosfets with jumpers in place of the resistors. The lamp matrix column section of that board is heavily baked, and heat will just continue to make it worse. The mosfets run much, much cooler than the resistors, and they won't continue to cook the board.