I have gone in May a few times, I didn't find it too busy in terms of availability, but I guess it depends on where you want to stay. If you have serveral choices you may be okay.
However, there have been quite a few discussions on how difficult it is getting to do short notice booking. I haven't tried it (I'm one of those who panic if I don't book 11 months in advance). Sorry, I may not be of any help in this case.
However, I will let you know that if we ever had to change our dates in such short notice and we wanted a room onsite, I believe I could always count on SSR. But that's only my opinion.