I'm trying to book a hotel on the top of Tai Shan (Mount Tai) but there only seem to be three hotels that can be booked online. These are all booked for the weekend. I know there are more hotel options on the mountain, but I don't want to leave anything to chance. For some reason, none of the travel agencies want to help me book a hotel because I'm not in one of those lame travel groups with the funny hats? In addition, the local agents want a down payment before I get there before booking, which is not practical at this point. Am I SOL this weekend or is it possible to get a hotel booking for the top of that mountain?