I've been a DMT for 8 years... To work in the gulf you have 2 options:
1) go to commercial diving school and work for a dive company as a diver. For the dive companies you are a diver first and a medic as a bonus. You'll get an extra $1-2/hour over your diver pay. They don't hire strictly dive medics.
2) Be a paramedic and get your DMT. Work for a contract medic company that places you on a barge or oil platform as a medic. The dive medic part will help you get hired and will get you on dive jobs instead of normal oil rigs. They will most likely not hire anything less than paramedic, because that's what oil companies require to be on their projects.
I've done both routes. I spent 7 years as a diver/dive medic and absolutely loved it. I broke my leg and switched to being just a medic last year. To be a diver you're gonna spend around $20k on dive school and be gone A LOT with no set schedule... But I made between $65k-$85k working about 7 months a year. As just a medic I worked 2 weeks on/2weeks off and made around $60k. The biggest perk is that everything is payed for while you're offshore and if you have the set 2 weeks off you can work on a truck while you're home.
I don't know what kind of class DAN offers, bit if it's just their 'rescue diver' class, that won't cut it. You need to find a NBDHMT Diving Medical Technician course. It's a week or so long(M-F 8-5) as long as you have your EMT. All the commercial dive schools will have it. CDA in Jacksonville, FL, Oceancorps in Houston, DIT in Seattle, College of Oceaneering in Cali, etc. It includes decompression chamber ops, treatment dive tables, IV's, Intubation, drug admin, suturing, foley cath's, and of course all of the dive science/physics/medicine.