it looks like a discount factor would settle the agent's problem

Maybe not, if you believe that tomorrow you can self-modify into an agent that can clean the room better than you. (Better enough to offset the discount factor.)

I do not understand the Löb's theorem, so I cannot help you here. I agree that my explanation doesn't seem very impressive, but I cannot tell if that is because the original article is unimpressive, or because I am only able to understand the unimpressive aspects of it. :(