A lot of busy, high-profile people (Noam Chomsky, for example) have done off-line AMAs. That is, commenters will post questions, and upvotes will determine the best/most popular ones. And then, answers for those will be posted all at once, maybe even as a different thread if enough time has passed since the questions were asked.

That would have been an excellent model to follow here, and probably would have meant more time spent answering each question (for the President) and higher quality questions getting upvoted (since there's plenty of time for the collaborative filtering process to shape the question-space).