five commits: improve the ordering and the naming of some types

The first patch undoes the rest of a commit from seventeen years ago that was partially undone five years later.

The second patch drops sixteen redundant level specifications from one 8-level type.

The third patch renames two 8-level types, to be more understandable.

The fourth patch reorders some includes so that types are ordered roughly in the order of increasing number of levels.

And the fifth patch relocates a misplaced 8-level type, and renames it in the bargain.