A vessel about that size who had to draw 4' tied up to the end of Grande Caribe's dock about 4 years ago while they stayed there for a few days. Couldn't have been much water under the keel. I think I watched her leave and of course she stirred up a lot of sand. Their dock is very close to the channel such as it is.
There was a local Belizean who took care of the docks but I just can't remember his name, he would know. They are sponsoring an off shore fishing tournament and are the only official weigh station in Belize so someone must have that info. Give them a call or send an email. Good luck.