Has anyone ever had to turn down an interview because of really bad timing/conflicts with the interview dates offered? Things you can't cancel without jeopardizing other very important things (like a current TT job)?
My inclination is to just tell them the reasons why I can't make the dates they offered and see if they want to either move on to another candidate or work with me on it. It is a good potential opportunity but also would be a lateral move and I don't want to risk my current TT position because of some specific events that would be very unusual/problematic to miss.
What would you do?