If March isn't a particularly special time for you other than the weather aspect, I suggest September. We've gone twice (07, 08) and the weather was fantastic. It's low crowds too so you get to do a lot of things without much of a wait, if any. (we walked right onto Pirates of Carr in the middle of the day)
My DH refuses to go on any vacation unless he can lay in the sun by a pool and he enjoyed it alot. There was the occasional sprinkle of rain, but it's FL, so that is to be expected. It didn't bother us too much since DH grew up in FL and we lived there for a few months, so we're used to it. Just something to think about!