As to where Scotty and Kirk ran off to when the transporter malfunctioned, I figured it was to the transporter in the engineering hull and thus out and to the starboard corridor. There's room on the starboard side and also if they needed to go down a ladder one level to the space between the engine room and the cargo bay for a transporter to be placed there.
The issue with the timing and layout of the Engineering/Transporter Room/Corridor scenes is an interesting one. We're not given any on-screen indication of where the Transporter Rooms are, but backstage materials put them in the saucer, and presumably the Engine Room is near the top of the secondary hull. Between leaving the Engine Room and arriving at the Transporter Booth a little under 9 movie-seconds elapse. I'm willing to grant that some time may have been lost in editing, but a transporter cycle just isn't that long, even in TMP.
I doubt that there is really time for Kirk & Scotty to race down the corridor in the secondary hull, wait for some doors to open, board a turbolift, call out their destination, wait for the doors to close, ride 8 decks upwards and sideways, get out of the turbolift and run down enough corridors so that Kirk can lose his way again later.
I'm sorry to say it, but Commander Sonak & Lori would have been mush on the Transporter Room floor before Kirk and Scotty had even got to the turbolift.
So, what else might be happening on screen? It struck me that Kirk & Scotty dash out of the Engine Room set in the direction of where the Transporter Room set is, on the stage layout. I do not know whether this was a deliberate choice by the director or a casual choice by the actors, but it got me thinking:
What if the Transporter Room really is just down the corridor from the Engine Room?
There's certainly plenty of space on the stageplan layout to place the visible sections of blue corridor, silver corridor and Transporter Room. However, whether we treat the painted backdrops as actual corridors or not, we would quickly run out of room in the secondary hull for the Transporter Room corridor, even on a 1164' length vessel.
So, what about the saucer?
The corridors would need a little shuffling to make the centre of the circle the centre of the Engine Room, but it still works:
The theory of multiple engine rooms on TOS deck plans have been around for a while, but as far as I know it's never been applied to TMP. However, it would solve the problem of the extra long corridor, the timing of the dash to the Transporter Room, and the reason why the console around the intermix tube would have anything to do with basic transporter functions (this last always struck me as odd). It would also explain the
dissappearance of the long corridor outside the Engine Room in TWOK -
because it was never in the secondary hull in the first place! The TWOK Engine Room is clearly in the secondary hull, as shown by Khan's attack. A lot of TMP's engineering scenes took place there too (since they involved the Warp Drive) but the initial ones - they are firmly in the saucer, IMO.
I should add that I don't see the saucer's Engine Room as one that generates power. The original function of the Engine Room tube (from what I've read) was simply a "Power Transfer Conduit" of some kind - no warp core in THIS vessel, thankyou! The saucer's horizontal PTC operates in reverse, compared to the secondary hull. Instead of sending power to the V-shaped split, this is where power is delivered, either from the main M/AM reactors or the Impluse Engines (or both). The energy can then be directed to wherever it is needed in the primary hull.
The purpose of the Saucer Engine Room is to control and regulate energy transferred via the PTC for use by saucer systems. Systems like the large sensor/deflector cluster on the saucer bottom have their own direct PTC feed. The area above the Upper Engine Room would be where the PTC is split into feeds for the upper phase banks and secondary shielding for the Bridge. The saucer has a much larger surface area than the secondary hull and the deflector shield grid would need a lot of power in its own right. Plus gravity, life support and the various control systems etc would all combine to draw a great deal of energy, more than justifying the existence of a PTC in the saucer.
The Engine Room would have to be located fairly high up in the saucer to fit the 5 decks seen below when Kirk peeks over the railings. I think however that the upper part of the saucer disc would allow both the vertical and horizontal PTCs to squeeze in, even on a 1,000' long ship. The Main Engine Room may be 12' high, but the decks seen below don't appear
anywhere near as tall. In fact in TNG the
Lower Engine Room set was
only 7' tall so it would not be unreasonable to think that TMP's were at least similar. I don't know how much sense this makes from a deck layout perspective, but 7' decks would at least allow the Saucer Engine Room to fit in a 1,000' hull.
Since the location (or quantity) of the Transporter Room(s) is never made clear in TMP, relocating it to the top of the saucer disc is not a problem. When Kirk is in the corridor after the transporter accident, he asks the way to "turboshaft 8" which might indicate that it is on Deck 8. To me however, such formal nomenclature merely reinforces Kirk's unfamiliarity with the refit vessel. The novelisation says that Kirk had studied the blueprints and plans of the refit project, and if this is true then he may well remember that turboshaft 8 is the one that runs up the starboard Bridge door, even if he can't recall specific deck layouts (or what deck number he is on).
So, the Transporter Room may be located much higher up in the saucer - indeed, TWOK shows us a "D" on the turbolift doors after Kirk & Saavik are rescued. Now, the "D" may or may not relate to a deck number...but that's a debate for another time!