The idea of the Lincoln-Douglas debates are deeply ingrained in the American psyche, but I think it's time to face up to the fact that that era of the debate has passed.
Instead, I wish the candidates would do a written debate. I don't just mean "Send them each a bunch of questions and publish both responses", I mean an interactive series of answers and rebuttals. Randomly choose half the questions to send to the one candidate first, half to the other. Set some word limit. (And if were up to me, I'd tell the candidates that it's a hard word limit; send me 600 words instead of 500 if you like, but I'll just cut you off mid-sentence...) Stop at two or three iterations. In the internet era, I'd give them as many hyperlinks as they wanted and not count them against their word count, and invite the candidates to continue after the official debate on their own websites, if they like, giving both of them the last word.