Recapping a 3000 is relatively easy. Battery corrosion repair is not. I've done a lot of repair on boards like this, and depending on the level of corrosion, it may be too far gone. That said, the Amiga stuff is well enough documented that it's possible to make things work that you wouldn't think could be fixed, simply by virtue of being able to know where the traces were supposed to go before they got eaten.
What I think needs to be done is re-layout of the Amiga 3000 motherboard. Populate it with SMD commons, then sockets for the customs. Keep it close to 1:1 with the original just no lithium battery. I was at the premiere of the Viva La Amiga documentary at Magfest and talked to Dave Haynie a bit about this. A3000 is a 4 layer PCB with 2 layers just being power/ground. Are the schematics out for the A3000? I assume so.