Yes, it's definitely not an easy fit as Mytran
had provided a "corrected" illustration of the phaser room studio set in your thread
What I really like is the alignment of the door frame, the phaser coolant bottles and the (unseen) master control panel Tomlinson operated as these would fit nicely within a circular structure (I presume the phaser coolants to be at the bow and in closest proximity to the actual ship phasers), assuming the weapons monitor console (between the two vertical power pipe conduits) is the center.
I'm starting to wonder if the three phaser batteries / banks (port, starboard, midship) are below
and in the sensor dome (according to the dialogues in "Balance of Terror" and "The Doomsday Machine" these batteries or banks have first to be charged / energized before the phasers can fire) and the two power conduits we saw actually charge the port and starboard phaser bank (while a third unseen one in the back charges the midship bank).
A general problem with this room or set is the waste of space between the console and the phaser coolant bottles. Almost looks like the floor panels in this area could be lifted up to do repair and maintenance on the actual phasers while still leaving enough space for other personnel to walk around this area.
Still doesn't answer the question how Spock got down there that fast. Maybe a fireman's pole kind of thing within some kind of Jefferies Tube?