you will be fine with the tires you have.. the mac woods dune rides use airplane tires (bald like slicks) and actually the less tread the better because you dont dig in. i have been there every year many times since i was 16, all you need is state park sticker ($6 bucks for a daily) an orv sticker ($16.25 for a yearly) a rectangle orange flag at least 10 feet off the ground on the front of your jeep, and gas. You will not have to sign any waivers or anything. keep your tires closer to 10psi and you will go anywhere. Also like everyone else said stay out of the water holes, they will swallow your jeep whole, I have seen it many times.
BE SAFE AND HAVE FUN!!!!
ITS A BLAST UP THERE I JUST WAS THERE FRIDAY NIGHT WITH MINE.