First off be aware Mardi Gras is March 5th this year, which may make it difficult to find a place to stay that weekend. I recently looked up the availability at Palmetto Island state park which is located south of Abbeville, LA (about an hours drive south of Lafayette) and they had availability from now until Mardi Gras week, some weeks nearly empty then booked solid for 3-4 days around Mardi Gras. Palmetto Island is a nice little state park, though the mosquitoes can be an issue. If you prefer state parks, instead of doing Holly Beach, you might consider crossing into Texas and staying at Sea Rim State park, it has been a number of years since I was last there, so can't comment too much on current conditions. There are also several walking trails (board walks) in the national wildlife refuges along the Louisiana coast, that are nice unless you get caught between two alligators, as they like to sun themselves on the walking trails, also don't take dogs on the walking trails for the same reason. Also be aware that the petro-chem construction industry is booming here in SW Louisiana right now, particularly in the Lake Charles area so all the commercial rv parks are filled with contractors, and they are building new contractor rv parks as fast as they can. I know of at least 6 new ones in the last 2 years, all of which fill up within days of opening.
I too would suggest a couple of Louisiana adjacent options just across the river into Mississippi, first would be the Vicksburg battleground (though it is not large RV accessible), and secondly given your date range consider the Natchez pilgrimage https://natchezpilgrimage.com/spring-tours/ . Unfortunately Louisiana does not have the greatest state park system, as it is historically underfunded, most national forest camping in the state is primitive or dispersed, also most of the COE campgrounds are in the northern part of the state. There are a few exceptions, when it comes to public RV camping, there are some municipal parks with RV sites that are nice, as well as a few oddballs, like the Indian Creek Recreation area http://www.ldaf.state.la.us/about/indian-creek-recreation-area/ located south of Alexandria which is operated by the department of agriculture, not to be confused with the commercial Indian Creek campground north of Hammond.