The Romex wire worked fine, it just looked very ugly. Again, it was only a temporary hack so I could test the CPU right away. I only had #6 machine screws on hand, which were too large, and the first local hardware store I went to didn't have anything smaller than #6 for some strange reason. When I tightened the Romex, I twisted each side little by little so the heatsink would tighten evenly against the die. It wasn't pretty, but it worked absolutely fine.
I was finally able to source some smaller size nuts and bolts locally. I ended up getting #4 screws, mostly because that's what was available. I tried to find appropriate springs, but couldn't. I would have liked to have used springs to apply the pressure, but the specific kind I need wasn't found locally. I know I can order assorted springs from places like Amazon, and on the cheap, but I really want to examine them in person. For example, if the spring is too weak then it would be pointless to use. So I ended up just using the #4 nuts and bolts, and was just careful not to over tighten them.
As a lucky coincidence, the nuts that I got fit perfectly in the slot of the heatsink. All I had to do was spin the screw to tighten the nut! The screws that I got are excessively long, but it's not matter. I did put a dab of blue thread lock on the nuts just to be sure they never loosen up. This heatsink doesn't have a fan (there's a fan shroud from the PSU in this system) so I'm not worried about vibrations loosening the nuts, but I figure they could still loosen over time anyway.
When I tightened the nuts, I did so in an X pattern. I made them really snug, where they pretty much just started to get tight, and then stopped.