I like the idea of each candidate selecting a moderator to ask questions of the other candidate. I also think the local parties should each get half the tickets for the audience. That way you get plenty of partisans in the crowd both ways. Regardless, I do agree the debate shouldn't be set up and run by some news network of journalist hacks. You could still include rebuttal, but the moderator that asks the questions handles things until the next question.
Should each candidate pick the questions to be asked of the other guy? Or just let the moderators pick them?
One of the Republican Primary events had each candidate speak and answer questions for about 30 minutes individually with a single moderator. I thought that was a good change of pace.