We've dove Belize many times in December and more recently have switched to going in late January. Somewhat due to schedule but also that TIR used to offer a pretty good deal during the shoulder season before Christmas. December weather is more inconsistent for sure. We've had a few trips interrupted by a cold front dipping south, the worst resulting in no diving for 3 days. Some of the trips the weather was very good and no issues, definitely a little more of a possibility. January's weather is much more consistent and so are the crossings out to the Blue Hole and Half Moon. Not much in the way of water chop in January unless the wind/weather switches and comes out of the north.
We haven't dove from Ambergris, only the outer atolls (Glovers, Turneffe, Lighthouse). I think most would agree that the better diving is from the outer atolls. Most Ambergris dive ops offer trips out to Lighthouse and Turneffe, it all depends on what you are looking for. Some people are disappointed in the Blue Hole dive, I would suggest you dive it for what it is. It's about the formation and the huge stalactite formations, now under 135' of water. Not much in the way of marine life, maybe a couple of sharks. I think I've dove it 11 times and every time has been a little different. The Half Moon and Lighthouse dives after the Blue Hole are great. The picnic lunch and shore interval at Half Moon make for a great day.