I am ridiculously picky about my BBQ. Ask my WDWCP roommates -- it goes far beyond the point anyone could ever consider being reasonable. I spent 5 months looking for a decent barbecue place in Orlando, and the closest I found was Bubbalou's Bodacious Barbecue.
It's a chain, but at least it's a local chain. I've only been to their Winter Park location, but I hear that they're either opening or planning to open one on the main drag in Kissimmee. Anyhow, it's pretty solid barbecue; good brisket, and a killer hot sauce.
Edited to add that the closest location to Disney is 5818 Conroy Rd, which is basically the interesction of Conroy and Kirkman, north of Universal.