Try booking for 3 or 4 nights and see if you can get in, then cancel the extra nights.
I was having a heck of a time getting just Friday and Saturday night at the Fort in December.
I had a discounted reservation for Wed and Thursday, and a discounted reservation for Sunday, Monday, and Tuesday.
Was willing to pay rack rate for Friday and Saturday, but couldn't get ANY availability.
Then I tried for for 3 nights starting Thursday and availability came right up!
I then cancelled Thursday night a couple of days later.
You could try for Fri through Tuesday, then check out early.
Carol