I can not vouch for the SeaSchool program but it seems like a lot to pay if you already have 3 years cooking exp.
Only the large US flag cargo ships, which are almost all union carry a real stew dept.
Besides that, plenty of tugs & OSV's carry a "Cook" but they usually expect the cook to handle/throw lines, etc in addition to making the meals.
Anyways you will need a MMC, STCW-95 BST and a passport.
If you really want to start over, look into the SIU U/A program in beautiful Piney Point, MD.
If you go through the program you will come out a "Certified Chief Cook" and be qualified to work on the SIU contracted ships... I bet you will make way more doing that than working offshore on the rigs.