Meghan,
We went through our travel agent who contacted the WC and found out available dates within a couple of hours. It seems to be a lot easier to communicate through our travel agent. Also all my guests are going through our travel agent so I don't have to organize anyone.
As for the time of year, I googled usual weather for those months. I don't remember Jan or April, sorry. I chose May because kids are in school so there will be less people at the resort.