Once upon a time, I found a way to select multiple headings in the Navigator.
(Not at all sure how I did that, can't seem to replicate that functionality now.)

When I did and applied promote/demote to the collection, the results were much
different than expected. (I expected everything to move together, but the
results were disjoint, instead.)

Of course it may be that was I dreaming. In that case, this request has two parts:
 a) Allow a range of headings to be selected
 b) "Do the right thing" when promoting or demoting the entries in that range.