"This is just one of those things I intend to "squint" at, because otherwise it is a continuity nightmare!!!"
You mean like this
(alien entity where Emergency Manual Monitor should be)
(alien entity opposite 'cathedral') versus
(alien entity next to cathedral, balcony would be near the cathedral similar to the suggestion of the shot from "The Ultimate Computer").
However, if there was one additional engine room where the cathedral is (facing forward) providing the power supply for the main sensor / deflector you could take the strange shooting angle from "The Ultimate Computer" plus the one (of the three contradicting angles) from "Day of the Dove" to match the departure of the alien entity through the engineering hull in the original TOS shot.