Couldn't the charity just rent the week from you in exchange for FMV, and then you voluntarily donate the cash back to the charity and take the deduction?
You should try running a charity where you pay people cash and expect them to pay it back to you.
Let us know how that works out...
(You can always rent a week that you own for cash and donate the cash for a deduction. But once people get the cash, sometimes they start feeling less charitable. )