So, after disassembling my clock, and disecting the light bulb, and remembering the pain of swapping my dummy lights to leds in my buick which used bigger sockets, I decided against modding the socket. Instead, I tinned the brass contacts that the light bulb uses on the board ("tinning" being a fancy word for spreading some solder around on a surface) probed out + and - with my meter and then soldered the led and resistor directly to the board.
Works without a problem, except for a hotspot. But, a led modding trick I read somewhere, is to use sandpaper to rough up the surface of the led, I've gotten them almost completely white before in the off state, and when it lights up instead of glaring straight out it glows more evenly. I plan to do this once I get some free time to try and pop the clock out again