So here's the spot where the largest amount of rust has accumulated.
I'm thinking that painting it is probably going to be the best idea. I had to take most of it apart anyway to re-pack all of the bearings and (soon to be) install a new chain and new handlebars, so taking off the last few components and sanding/priming/painting isn't that much more effort in my opinion. The thing that really pushed me to this is hearing that it was such a low end bike anyway and has zero collector value so I may as well enjoy what my own bike looks like, right?