expression manipulation - How to make arbitrary transpositions of associations and datasets

Is there a general Transpose for Dataset/Association that will transpose arbitrary levels, such as

Transpose[array, perm]

which will permute the levels of array according to the permutation perm? One seems to be able to use Transpose[ds] to transpose levels 1 and 2 and Map[Query@Transpose, ds, {n}] to transpose levels n+1 and n+2. But they only work on "adjacent" levels. To transpose levels 1 and 3 (i.e. perm = {3, 2, 1}), I seem to have to do something like the following

Transpose[Transpose /@ Transpose@ assoc]
Transpose[ds][Transpose, Transpose]

Is there a general way to do this for an arbitrary permutation of the levels of the data?

(I give a solution below, but as I'm learning how to use Dataset, I figure there are better ways.)

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