It's the placement of the room at port or starboard side of the saucer that we have a difference of opinion and you'll find no visual evidence to support a conclusive right or wrong answer, IMO.
We do see the corridor leading to the Engineering Control room in two scenes with Kirk and Spock in "The Naked Time", the area in front of the Season Two/Three engine room (you placed on the port side and which they must have passed) simply is not there.
Add to this that the enter scenes of the Engineering Control Room,
provide us with sufficient background information (near the floor) to conclude that the Season One studio set blueprint and the alignment of the Engineering Control Room is accurate as shown and seen on these set plans.
The Thermians might not have had access to the studio set blueprint but their analysis of the "original documentary footage" would have yielded an exact reproduction of that blueprint, IMO.
If you prefer to have it differently that's your choice, and frankly, I'm grateful you did it your way as this was a contributing factor to inspire my deck plan project.