Yes, I think it's something like 60 teams? Have you only checked through the online booking sites? They buy so many rooms and may have run out. We have better luck with the hotel itself...not even the toll free chain number...which retains many rooms to book itself, aside from the online sites. We have found many hotels competitive with the online booking site rates nowadays, especially if you ask for AARP or AAA rates. You might also try the specific hotel's site...not just like expedia, travelocity.
This is also a big weekend for getaways...the long weekend, first of the fall. Kind of like Memorial weekend being first of the summer.
Click on your weather to access weather from different cities and see if it's what you imagined. Some pools at the beach close early October. You might check if pools are open...they generally have a common closing time...so that you know if you should even be searching for hotels with outdoor pools.
It can still be nice and sunny, good for sitting out in light summer clothes sometimes...occasionally even in a swimsuit. If the pool is closed and the access to its deck as well you might find a chair on the grass to get some sun. I see the temp in W-S at the time of your trip is an average high of 74, average low of 49. It could take a while to warm up but a sunny day with not much cloud cover can give you a tan quickly. And we like those days that don't require baking in the sun.