I wasn't able to give an immediate response to the new posts; I'm preoccupied with my college classes, and this project is more or less in the backburner.
Thanks for the detailed instructions, @Gordon. I currently do not have soldering tools to remove and attach electronics, but I could get them a few weeks from now. This is going to be my first time modifying PCB boards, although I have some experience in soldering and the proper equipment to perform it.
@kri100s, the links you have provided seem to detail a manufacturer's component. I could sample it and design a PCB to mount it to the analog pins, but I'm not sure what other components it would need (it has 56 pins which is a little intimidating). I don't have too much experience with electronics and I'm pretty terrible at reading PCB schematics and block diagrams; in my spare time, I'll try to improve reading these diagrams.
Eventually, I want to create custom straps with embedded electrodes for the sensor. If I go the extra mile, I could also add a new HRM. For now, I'm seeing if I can modify the watch to accommodate just the skin-conductance sensor.