"Maybe the usual turboshaft route is undergoing maintainence and it had to take the long route round?"
is the kind of rationalization I'll do my best trying to avoid whereever possible.
The problem with the transporter room is its outspoken rectangular basic frame so to speak. Mirror it to the port side Season One "Engineering Control Room" ("The Naked Time") and it will look better than looking displaced at an angle within the saucer.
While it's still just an option, I imagine the "Elaan of Troyius" transporter room (i.e. the one from "Charlie X" and "This Side of Paradise") to be on the starboard side of the saucer stern, the yellow door opposite the transporter room's door would be an access door to the back of the wall panels of the Engineering Control Room.
In contrast the transporter room from "Day of the Dove" would be near the "Elaan turbo shaft" but around the corner (these two transporter rooms would be head-to-head with their transporter platforms).
To have two transporter rooms in such close vicinity (and next to the plasma energy feed from the engineering hull!) would - again - merit the door labels "transporter section
Of course, there wouldn't be place for a second Engineering Control Room (necessary?) but I wonder how this kind of arrangement, despite being screen-accurate, would look like.