FWD isn't necessary but you have to be smart about it. Keep moving, even on packed sand. Some entrances/exits are more passable than others. Watch where you park it as far as high tide line and how packed the sand is near the dunes.
I don’t think there should be any problem. We unhooked the Jeep from our diesel pusher, but I’m confident that it would have been fine if we had kept it in tow. In short, we had as many drive wheels as your f350 and we were fine. I say go for it! :-)