I agree with JRD. It's not that the boat isn't big enough, it's also the fact that it has an open deck and it's not made for that type of crossing. My understanding of the Gulf is that storms are frequent. You might find it hard to locate a reputable captain willing to cross that body of water in that type of boat.
Hopping around the coast as JRD suggested would certainly be a safer approach if you want to go by water.
Although I have no idea where to start other than a Google search, you might look into container ship transport, too. That mode of moving boats is not uncommon.
For weather, you might start here: Sailing Weather - Marine Weather Forecasts for Sailors and Adventurers - PassageWeather