With regard to the 22-man evac transporters, I'm in favor of them. I suggest that the actual use of them is very power intensive and, when you're trying to pull your ship out of a crash through an atmosphere, you want as much power as possible feeding your shields and engines. In "The Apple" Kirk was ordering Scotty to "crack out of there with the main section" to get away from the planet with Vaal, quite the opposite strategy than beaming the entire crew down. In "The Savage Curtain" the surface of the planet wasn't hospitable, except for the patch of ground the Excalbians made habitable for purpose of their trial pitching Human conceits of Good and Evil against each other. So, evacuating the crew to the surface of the planet in this case is also a bad move.
In "This Side of Paradise" the drugged up crew is mutinying and evacuating the ship. Though we see one line of persons out the door of one transporter room, who's to say that the other 6-man units and the 22-man units weren't also being used? In "The Doomsday Machine" Decker claims that he had to beam down his crew to the fourth planet. It doesn't seem like this took a very long time to do (it does
seem to me that Decker is regretting a rash and hurried decision... YMMV) so, though there is no specific mention of 22-man transporters, I posit that it could stand as circumstantial evidence to support their existence.
in favor of the idea, that I'm including them on my own deck plans project. Here's my design for them... which departs a lot from the FJ approach, but i think this is more in line with the other transporter tech we see as it has the surrounding chamber like most other transporters tend to have and FJ omitted.
How I have this set up, the corridor basically open directly onto the Evac transporter area. The operator's console is elevated a bit to make sure the operator can see what's going on with everyone. The outer wall is lined with cabinets that store emergency gear. Both sides have stairs where people can come up from the deck below. The area is open so there's plenty of room to get people staged up. Anyhow, this is just my take on it. I'm not sure how it would fit into your "screen-only" vision.