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OK, I think I can see why the numbering may not work the way I want it to. It is rigorously hierarchical. Perhaps another approach could be to take the Sections out of the hierarchy altogether, and just manually number them? Is there a way to insert a string at points in the hierarchy to give the impression of a Section title? Like this:

Chapter 5: more stuff // numbered
5.1 Why use more stuff? // numbered
Section II: Moving on // not numbered
Chapter 6: Advanced techniques // numbered
6.1 Understanding advanced techniques // numbered

Any other solution would be welcome (well, actually, any solution at all).