This room thing gets goofier and goofier, through no fault of Jim's, btw. I just booked four nights, June 3-6. After many machinations relating to what type of room was available at any rate each night, here is what I learned:
1. There are no king rooms available on the 3rd, period.
2. There are no double rooms unavailable on the 4th, period.
3. There are double and king rooms available on the 5th-7th.
So, I could not opt for king the whole time, and if I want to maximize the double room nights then I would have to change rooms twice. Based on all of this, I booked a double room the 3rd and then a king room the 4th-6th. Gene and I will just be that much closer those nights. The very nice booking lady, Mary, told me to check back in later to see if the reservations ease up and they might be able to get me in one type of room the whole time.
Bottom line: book something NOW if you may be going.