Well, I'll be damned. The operation was successful... the X-Clamp fix worked. I spent about $15-20 or so to get everything I needed, and I have a good amount of random stuff left over. I did spend about 6-8 hours of my own time (mostly reading and going to get parts). Anyway, at this point the unit is completely working, and so now I'll just have to see if the fix sticks or not.
In any case, I'm pretty stoked. I was originally thinking it was maybe 3-to-1 against, but maybe I'm just a bad XBox360 repair handicapper. Anyway, I am going to have a celebratory beer now.
Seeing as how my XBox is still working after over an hour of play, I figure I should put up the link to the repair instructions I followed. I did have to make some minor modifications (i.e. I did not follow the instructions 100%, but it was in areas where I used my best judgment given the parts I was able to find -- for example, I was unable to find 1mm thick nylon washers).
Llama's X-Clamp Fix