Thanks to Jennifer of Gluten-Free Jacksonville, I learned that Campeche Bay Cantina in Jacksonville Beach now has a gluten-free menu.
I haven't been there since going gluten free but it is a restaurant I liked in the past, so I'm looking forward to trying it out. The gluten-free menu, which you can find on the Campeche Bay website, has a pretty big selection.
It sounds like they are well aware of cross-contamination issues. A note at the top of the menu warns that the corn chips are fried in the same oil as flour tortillas. It also says "when ordering from this menu please ask for Manager assistance." They don't even want us to rely on servers.
It all sounds good.