Good news! I spoke with my local HD and they told me that since I won’t be selling individual hot dogs to consumers, this would fall under the general food safety rules (i.e. catering) and not under pushcart rules. He suggested that I could pre-heat all of the dogs at the commissary and then transport them to the site in a suitable container; although he understood the desire to actually prepare the dogs on location as part of the show, so he said a turkey fryer would be fine as long as the food is being safely handled and prepared. He did reiterate that if I were to be selling the dogs individually that it would then revert back to pushcart rules.
I have a meeting with another health inspector tomorrow to actually permit my cart and will reiterate with him as well to ensure that they are all on the same page and that there are no nasty surprises later.