You'll definitely have to go back through Nassau unfortunately.
I'm a little confused by your post. Are you traveling with just your wife, and you're both going to do DIY? I've never been to Eleuthera, but have spent months on Andros in the last 10 years. For DIY you need to stay on the bights since there's very little fishing on the ocean side. One of your best bets would be to look into a boat to shuttle you to some flats in the morning and pick you up at night. Fishing the creeks isn't really a great option for the shuttle since pretty much all of the flats aren't something you can wade between, but you can do that in the bights in quite a few places. I'd also consider finding someone that can rent you a couple of kayaks. Honestly Andros wouldn't be my first choice for a DIY spot because of the difficulty of getting from one DIY flat to another. Acklins and Crooked are the easiest places to do a DIY in my opinion.
My passion for catching fish is eclipsed only by the fish's passion not to be caught.