You will have a better chance of getting what you want in late August, as most Southern schools start back up in the early part of the month. Also, if you're looking for a 2BR, you'll have a much better chance than if you want a 1BR or a studio.
Trading points with a HH owner is a good idea, but with the recent enforcement of the transfer policies, you will have to be a little more creative to do that.
Good luck -- you'll love Hilton Head!!