I did my Dean's List Interview at WPI.
The two judges there asked me numerous questions about I do on the team, my community service, my entrepreneurship, how I've inspired others, etc. They didn't time my interview, but they did ask for specific examples of some things while I was talking, even though the questions had obvious answers in the essay.
Although I went in with my normal team attire on, I don't regret the decision because I only saw one person there dressed formally.
As far as drive team conflicts, the other student nominee on our team faced the same problem. Rather than face a timing issue, he chose to do his interview at a regional that our team wasn't attending, but he would be at anyways. It's a little late to do the same, and the method obviously won't work for everyone's schedule; it's food for thought for next year, though.
Hope this helps!