I took the advice of manually filing the case.
Thankfully I have very small files, and, under a microscope, was able to file away the case much quicker than I had expected.
Once I got deep enough, I began filing downwards towards the pin and then took a small blade and scrapped away the remaining thing layer - I didn't want to continue filing and file away the metal pin.
I have a set of resistors with very flexible leads, so I soldered the lead into a socket (although now I'm thinking maybe I didn't need to), cut to length, bent the lead 90 degrees so it laid across the exposed pin, and placed a blob of solder.
It came out much better than I expected and quite strong. My only concern is in the future I may forget about it, attempt to remove the IC,and rip off the pin. I considered soldering a pin at the opposite end, but these sockets have flimsy pins and I fear they may break, so using epoxy or soldering additional pins may result in an issue should I ever need to replace the socket.
The sockets I've come across at old jobs were much more durable, the sockets I've bought at a local electronics store made by Philmore look like the pins are made from much thinner metal.