I almost forgot about this... while I was at E3 and stopping by the booth for id Software's Q3A mission pack, I got to talk to Tim Willits briefly. Here's what happened (paraphrased of course):
Me: "So what will id's next game be after Team Arena?"
Tim: "We'll start working on out next full game."
Me: "Any chance that the new game would be Doom2000?"
Tim: "I can't really say anything about that."
Me: "So you neither confirm nor deny the rumors?"
Tim: "I'd lean more towards deny."