Assigning a menu is one decision per item, and the only hard ones are the items two counters have always both been able to make.
Before a venue can take a single order from one menu, every item on that menu has to point at the counter that makes it. Most of the menu assigns itself. Bottled beer goes to the bar that keeps the fridge, the pulled pork to the kitchen with the smoker, coffee to wherever the machine is bolted down. A manager can walk a full menu in twenty minutes and be sure of nearly all of it.
The work is the short list left at the end: the items more than one counter has always been able to make, and that nobody has ever had to settle, because until now the guest settled it by choosing a queue. Somebody standing between two bars that both pour the same lager picks one, and the question never gets asked. A guest ordering from a menu cannot pick, so the venue picks for them, in advance, item by item.
The rule that keeps a service clean is one item, one counter. An item with two owners is not twice as likely to get made. It is an order that arrives in two places and gets made twice, or one both counters assume the other has. Neither is a problem you can fix on the night. When two counters both want an item, or both refuse it, four questions settle almost every case.
Occasionally one owner is the wrong answer. A site with bars at opposite ends of a field, and one lager everybody drinks, should not send half the ground on a walk because of a routing rule. The fix is not to assign one item to two counters; it is to make it two items, each named for where it is collected, in the same words as the signs above the counters. That turns a hidden routing decision into a visible choice: the guest picks a collection point instead of guessing, each bar still sees only its own lines, and the totals tell you which end of the venue was drinking. The cost is a longer menu, so duplicate only the items where the walk is real.
An assignment is a document before it is a setting. Print the menu grouped by counter and have whoever runs each counter read their own group out loud before doors. Two minutes of argument at a desk is cheaper than the same argument conducted across a crowd by two people who are both already busy.