"He who marches out of step hears another drum." ~ Ken Kesey
if the art supports it, use make a vinyl stencil and use the high temp spray paint made for BBQs.
Depending on the complexity of the art, it may be easiest to have someone cut a frisk or masking film and simply paint it on. As for the paint, as noted most Epoxy Inks will handle high temps and Epoxy readily adheres to almost anything. The question may be how much you want to invest in the job if its a one off or even a few. Buying a qt of 2 part epoxy ink to print even a dozen BBQ's means losing money, unless you can find other ways to use the ink in the future.