I installed the carburetor to intake manifold gasket and new spark plugs today. This is what the plugs looked like:
I cleaned them off a couple days ago, but decided to replace them to see if that helped at all. Between the new plugs and the gasket, I think it is definitely running smoother. Not as smooth as I'd like, but smoother. I took a video of it idling. It sounds like I am getting a misfire maybe every once in a while. Any ideas? Here's a link to a quick video:
https://www.dropbox.com/s/2jptj7fnqm..._7368.MOV?dl=0
I also replaced the fan belt while I was at it. As you can see, it was definitely worn out and I didn't want to risk taking even a quick drive and having it break.
Next steps will be to install the seat belts I ordered and to get the spare engine up on a stand so I can try to get it to turn over.