I would not do close to shore. From what I understand you will get beat up until you get 100 miles or so. Then you hit deep water. Port A 50 miles to deep water, Port Lavaca 150 mile and Galveston 100 miles. If you do the ICW carry plenty of fuel. Fuel is hard to find past Galveston to N.O. Most of my dock mates have done the trip more than once. From N.O Gulfport area you can cut across the gulf to Key West.
Its a shame you are not down here so you can do as I do "Pick their brains"
Remember one thing the Gulf can be a nasty, nasty place at times.