Before undertaking this project I must forewarn you that it is VERY VERY VERY tedious work, with a lot of "one step forwards, two steps back".
Step 1: IC Removal
Step 2: IC Holder
You can hit two birds with one stone if you choose to just cut the IC from the old PCB. That will save you de-soldering and soldering the IC. Just make sure to cut through PCB on the underside of the IC to break all existing connections because it is hard to know if the connection are what you need. If it is then life just got easier.
Step 3: Baseplate
Step 4: Pinouts
Step 5: Preparing for Soldering
Step 6: Soldering!
Use the thinnest enamel wire you have available on a spool.
1) The first step of soldering is to tin the wire.
2) Then place the wire on the pin and apply heat. There should be enough solder to hold. DO NOT APPLY SOLDER AT THIS POINT.
3) Tension the wire to the pinout board. Apply solder and heat to the pinout till the enamel melts away.
The final result should be a lightly tensioned wire from the IC to the pinout board.
NOTE: if a wire comes undone, do not try to resolder. Simple remove the wire and start again. It will save so much time.
Rest and repeat for all the pins.