You can not do day hops by using the safety fairways if you use the fairways you are committed to a likely three day offshore passage at 6 knots.
You CAN run along the coast in short hops anchoring offshore in waters of 20-30' in fair weather. You will see lots of shrimp boats anchored out at night too. Be careful choosing anchorages though because the Gulf is littered with buried and unburied pipelines everywhere, mostly unmarked.
You can also drop in to protected waters at the mouths of rivers and bays. Sabine, Calcasieu, Atchafalaya rivers, Vermillion, Terribonne and Barataria bays. Once near the mouth of the Mississippi River you can cut in at Tiger Pass, come in to Venice, cross the river at Pass a Loutre then up behind the protection of the Chandelieur Islands to Gulfport and on to Mobile along the Mississippi Sound. Navigation aids can be spotty in the bay's.
You are in the territory of sport fishermen who make day trips out to the rigs daily without issue. But they are not doing 6 knots though. I am going to make that same trip you are thinking of at the end of March myself. I will be on my boat this week through end of next if you would like to visit to discuss.