Removing the socket will be very simple, you can use desoldering braid and a standard soldering iron. A bulb type solder-sucker is a very small investment to make as well. Wick or suck the majority of the solder from all the socket's thru-hole connections. It may even come off without a struggle. If not, once the individual pins are pretty much loose, it's no big deal to use a pair of diagonal cutters or nippers to destroy the plastic socket in order to deal with each pin individually. At this point you should be able to get clean thru-holes for each of the 30 connections very easily.
Then it's just a question of soldering the wires onto a SIMM, practice on some keychain fobs: 256k SIMMs were > a dime a dozen and even 1MB SIMMs are nearly worthless today.
When you're confident, solder the wires to your larger SIMM, it's not like you can burn a leg off an IC in this process, edge connectors on PCBs are robust by comparison and the wide spacing almost ensures that you won't have any shorts. Test for them anyway.
Thread all thirty (two inch)wires through the matching holes in the PCB and then hot-glue the SIMM into the correct position. Soldering the wires to the underside of the Accelerator PCB will be a piece of cake, test for shorts and then nip the generous excess wire off after you're done.