I wouldn't use a belt sander, a belt sander would be too rapid a bit and leave divots in the deck. Also, the 2400psi might actually cut into the wood, you'll have to take it easy on the deck. If the deck was screwed down, you could remove the deck boards, plane them off, and reapply, and the results would be pretty great. Since you probably don't have a planer, and don't like the idea of removing each board...
I'd be inclined to say you are going to have trouble with the paint on the rough spots. Sounds like the deck was a bit rotten and paint covered it and protected it, I could be misreading you.
If I'm right about the rough spots, removing the paint is not only going to be difficult, but it'll expose some problems.
What is the deck made of? cedar? redwood? green treat? Let us know a bit more in a new post.