I've seen it mentioned on these boards before, but what do you think about asking your home program if they can find another time to interview? The days my home program interviews conflict with a lot of other programs, so I'm going to have to cancel at least one, and I'm not one of the people with 20+ offers.
You obviously can't ask another program to make an exception for you, but would a home program do that? Specifically, would they do that without thinking less of you as an applicant because you're trying to squeeze in extra interviews at other programs? I definitely like my program and would be happy to end up there, but I also want to make sure I end up somewhere next year and not in general surgery.