From an engineering point of view the "Eaternet" wired transporter would be the best option. Less moving parts = less chance of breakdown. It also would eliminate the waste of alot of internal volume on "dumb waiter" tubes. Nevermind reducing man hours spent keeping them clean and functional. If you are worried about power issues then simply shut the system down during red alerts. (who will have time to eat anyway?)
How the food is created prior to transport to destination, based on service time witnessed in the original show, I would go with some kind of replicator or device that worked with basic building blocks like generic meat, soy, flavor additives, etc.
The tribble issue is easy to resolve if they have a heightened sense of smell. They got to the location where the meals are created after being attracted to the odors through the airducts.