Having never fished Exuma I can't help you with that. But having done many DIY trips to Andros, Long Island and Acklins I can tell you that I never encountered any hostility on any of them.
Unless your heart is really set on Exuma I would take a look into Acklins. I think your opportunities to access a decent number of flats by car and find fish on your own are far superior to the other islands I've been to.
Vince at Cattaraugus outfitters (forum sponsor) offers a couple of DIY options you can also look at VRBO.com/Acklins .
Feel free to PM me if you'd like.