I believe You might as well give up on this query. To the best of my knowledge there is no rhyme or reason to classification of the Salvias or of the Lamiaceae in general. Most garden specimens have been hybridised to the point where they cannot be identified by any scheme. The 'native' Salvias have mostly been named by amateurs or by horticulturist who cared little for correctness. The so-called experts cannot offer a concise, workable key to identification; this I know because I have searched for over ten years for such a key. The best thing to do is have another beer and forget about identification.

Taxonomist:
I guess no one has the time to rework things so they make some
some sense. I understand that some of the Verbenaceae from genetic test are more closely related to the Lamiaceae.
Kew has been working on devising a better key for the Lamiaceae but have not started on the Salvias yet.
So back to having another beer.
Art

If you are near a library that subscribes to ProQuest Dissertations .., you can look up Jay Walker's work on Salvia s.l. and especially the Western Hemisphere groups.

Here is a link that might be useful: Jay B. Walker dissertation