I sail on the northern Gulf coast as well, and have done the trip from Biloxi to Ft. Myers, direct, as well as many other routes from the Keys and other points in south Florida to the northern Gulf coast. The trimarans you mention could safely do the trip with proper preparation. It is the weather and heavy traffic in the Gulf you have to watch out for. Leaving from Galveston would put you in the middle of a lot more traffic, oil fields, etc. It's much better to cross from points farther east. As for the trip to the Virgin Islands, you can't get there by sailing south from the Gulf coast. You first have to get around the Florida peninsula, then either island hop almost dead to windward using your engine most of the time, or sail out east through the Bahamas on a heading with more favorable winds until you make enough easting to then bear south on a close reach for the Virgins. This is a long offshore passage but much easier than trying to bash against the wind.
As to your question about other multihulls within your budget that can do the trip, I would advise you to look into the newer line of Wharram catamarans, (eg. the Tiki 26, Tiki 30, etc.) These are among the most seaworthy of small multihulls, the Tiki 26 having been proven in many transatlantic crossings and the even smaller Tiki 21 has circumnavigated, making it the smallest catamaran to do so. The Tiki 26 or Tiki 30 could be well within you budget, if you could find one for sale, or you could build it yourself. These catamarans are easily beachable, and while not trailerable per say, can be disassembled and brought home for maintenance or storage. They are also better load carriers for their size than similar sized trimarans, but you have to be careful with the weight issue on any multihull in this size range. Do a search for Tiki 26 and you will find a couple of blogs about the building and sailing of this design.