And, presumably, assign one district each to LA and NY?

I never said that?

But the formal statement of the problem, if the principle of indifference is to be useful, must generally be quite low-information -

Why does "the formal statement of the problem" matter? Reality doesn't depend on how the problem is phrased.

You seem to be trying to find an answer that would satisfy a hypothetical teacher not the answer that you would use if you had something to protect.

In order to get in the low-information mindset, it helps to replace meaningful (to us) labels with meaningless ones. In the first "formalization," all we know is that Julia Roberts could be in one of 3 named cities. Avoiding labels, all we know is that agent 1 could have mutually exclusive and exhaustive properties A, B and C. As soon as the problem is stated this way it becomes clearer that you can't just condense properties B and C together without changing the problem.

Suppose I instead called the options A1, B1 and B2. Renaming the options shouldn't change anything after all.