A brief clarification of traffic designations is in order. Traffic designations have absolutely no effect on what jobs are taken by what dwarves. A dwar4f will take a job based on straight line, as the worm tunnels distance. Once a dwarf accepts a job, he must path to the job. Traffic designations will not stop him from getting to that job. If he must path through a bazillion restricted tiles to do so, he will.
Eating and drinking are jobs. When a dwarf needs to eat or drink, they will select the nearest destination, calculating distance as a straight line between the dwarf and the job. Only after the destination is selected does path finding take place. If a destination is right next to a dwarf, it won't matter that he must path 500 squares out of the way, across a waterfall, and through a field of restricted squares to get there. It is still the closest destination, as the game figures it when selecting such things.
You can use burrow to restrict what jobs a dwarf will accept (aside from civilian alerts, burrows don't restrict where a dwarf goes, just where they accept jobs) You could, for instance, create a burrow that includes your entire fortress, except for the jails. Put everyone in that burrow. They will no longer see "Eat" and "Drink" jobs originating from your jail.