This requirement is clearly the bottleneck that would cause Scouts to back up in our troop as well, when you have a full patrol of new boys. We, like Twocubdad, also have various months where the outings are not organized in a way to allow for patrol cooking.
One can imagine a variety of methods to deal with this. A couple that we've done are 1) to have six-meal campouts, where two Scouts can fulfill the requirement, and 2) to throw in an extra patrol campout or two, just for the New Scout Patrol.
An obvious option is to:
3) Start assigning a head cook on campouts as early as possible. If not the first campout, then the second.
And then there are solutions that go along with creative interpretation of the requirements:
4) Allow them to cook for other patrols.
5) Break up the patrols into smaller groups (e.g. a patrol of 9 could become two patrols of 4 and 5)
6) Break up their meals over multiple campouts
I would not be surprised at all if there are troops that have multiple "patrol head cooks" that work together on a campout in order to allow more boys to check off this requirement, but that seems to clearly violate the spirit and letter of the rule.
Oak Tree