Almost the entirety of Smokey & the Bandit was filmed on location in Georgia, mostly within about an hour from Atlanta. There is a remarkable page full of details about the filming at atlantatimemachine.com, but unfortunately the site is only sporadically available. Its creator and owner, the awesome Greg Germani, was very seriously injured on his bike last year and so updates and regular site access will be quite a long ways off. You can visit them on Facebook, though: https://www.facebook.com/AtlantaTimeMachine
But yes, the Diablo sandwich scene was shot at the Forest Park Old Hickory House, one of (then) about twenty locations of the chain. Today, there is only one OHH left in Atlanta (Tucker) and one in Charlotte which has a review here at Roadfood. I'm not sure what other cities had one.
Very good detective work finding those old menus. We used to visit the OHH on Cobb Pkwy - it's been a Mongolian BBQ place called Jade Palace for decades - quite often in the late 1970s/early 1980s so I remember the look of that menu well. Of course, that was long before I learned to like barbecue, and I'd usually have a cheeseburger, which was far better than you'd think, and, as Old Hickory House dwindled and deteriorated, was probably a better option than the barbecue.
Maybe I should visit the Tucker OHH, for old time's sake.