Realistically, there was nothing that anyone in Belize, government included could have done to remove that boat from the reef intact and without doing much more damage to the reef. It would take a very large, long reach crane barge...the closest probably located in Louisianna. Cost of that , if the boat could last for several weeks until the crane arrived, would be far more than the value of the boat.
Most people overestimate the capabilities of the Government of Belize... about the same as a small town in the US.