When I saw the device, my instinct immediately said "likely to be GeneralPlus". They were the biggest "company you've never heard of making chips in things everyone has" of that era.

Not only would I have to solder all 48 tiny pins onto the PCB, I would also have to do it quickly enough to avoid melting the plastic on the sockets. I had neither the tools nor the skill to deal with that

Put some solder paste on the pads, line up the socket and reflow with that hot air gun you just bought. Preheating the underside of the board helps. The plastic is designed to withstand the brief exposure and you shouldn't be aiming the hot air at it directly, but instead at the pads and contacts.