I worked in Dinner Theatre for two years. It was definitely its own beast, but the biggest challenges I found were the actors balancing being waiters vs. being performers. Often shows would start late and intermissions would drag on past 30 minutes because the waitstaff duties took time. And, let's face it, some actors are not the most talented waitstaff. But when the money from the tables is the primary source of income, and the show pay is just over minimum wage, tips become the priority. Sometimes it felt I was in more meeting about tipping policies than ones about putting on a show.
As far as being in the back of the house and accessible, it can be tough. I am sure you know this already having done it for 3 years, but I would point out that even if the guests see you as one of the "techie" people, you're still representing the theatre and insomuch as it doesn't interfere with your show duties you should strive to leave a good impression and provide the best customer service that is feasible. I know I was stopped many times for a refill of water while I was on my way to the booth (especially since I was dressed in blacks like the food runners were). If I wasn't able to do it for them quickly, I'd try to contact the nearest person who could to make sure the guest is taken care of. If not, a sincere apology and explanation that you're not waitstaff goes a long way.