Agreed on Maxhappan. Beautiful grounds, clean rooms, great local management. You are right about no direct beach access, but you are NOT FAR at all.
About the fishing. There are a few great guides on the island who can take you on any type of trip (trolling, bottom/bait, fly). I suggest you look around when you get here, no real sense in trying to book beforehand because of weather et al.
Most/All of the fishing boats are not covered because fisherman generally need access to all sides of the boat while fighting a whopper fish.
Fisherman in Caye Caulker mainly work with skiffs, here is some more info: http://en.wikipedia.org/wiki/Skiff