And just to reiterate and be clear, I for one do not favor a saucer rim/impulse engine location for the Engineering Section just because FJ said so, but rather because of several self consistent clues from the show itself that indicate that FJ made the right decision. First, there's the previously discussed association of impulse engines with Engineering Section location from "TUC",
Not that I disagree with the location if we're using non-screen sourced info but wouldn't this be assumed regardless of the source that an engineering section would be associated with the impulse engines? The size of the section isn't really pinpointed so why couldn't it extend a good chunk forward and laterally in the saucer?
and second, there is the scene in "TPS" when the ship is at maximum warp, and Scotty is in "engineering" (were not told which one) and gestures behind him as he says "These engines are beginning to show signs of stress", and since nothing in the series suggests that the warp engines are anywhere other than in the nacelles/pods, this could be taken as further evidence that he is in the Engineering Section -in the impulse deck- and is gesturing toward the warp drive engine/nacelles suspended out there behind him in that general direction.
It looked like he was gesturing to the cathedral section about the stress (even then his hand doesn't really point that way). If he was referring to the nacelles (which aren't visible from his vantage point) he's pointing too low even if he were at the back of the saucer rim.
Of course, this would also indicate the orientation of this engine room, and that FJ got that right as well. And finally, for now, there's the aforementioned deck seven reference from "TDM" and from which "power failure in main energizers" is reported, which is consistent with an engineering room on that deck, which is consistent with TMOST/FJ.
The fun part then is figuring out where Deck 7 is
I think two different procedures are implied here?
Spock may already know that switching to bypass circuits (plural) is not an option, because as first officer, it's his business to such things, so the alternative is rigging (hay-wiring) a bypass circuit (singular) which would do an end run around the crystals altogether, but Scotty informs him that's not an option either because they blew the whole converter assembly.
But later, when Kirk, having been occupied with other things and not being aware of the severity of the situation, suggests switching to bypass circuits, Scotty tells him that's not an option either because they've burned them all out.
Since we are told earlier in the episode that a burned out circuit is tantamount to a burned out crystal, then it follows that burned out bypass (power?) circuits may involve burned out crystals as well?
It might however the dialogue for each failed lithium circuit is very specific:
SULU: That was one of our lithium crystal circuits, sir.
SULU: Another circuit, sir.
SULU: Another lithium circuit. Now supplementing with battery power, sir.
SCOTT: I don't know, sir. With those three lithium crystals gone
SPOCK: The entire ship's power is feeding through one lithium crystal.
KIRK: Well, switch to bypass circuits.
SCOTT: We burned them all out when we super-heated.
If the bypass circuits were also using lithium crystals they would've been called out as such, IMHO, and we'd hear of additional crystals getting blown out.
Then again, it goes back to whether lithium/dilithium crystals are needed for warp drive. Modern TNG seems to put that as a requirement but (jumping over to TNG) where would the TNG "First Contact" Cochrane get crystals for his warp ship?
So perhaps switching to bypass circuits normally involves switching to at least two back-up crystals, which means that at the point in the episode when all this is discussed, they have burned out a total of five crystal/circuits not three, as usually assumed. this explains why, near the end of the episode, Kirk says they need six crystals, because by that time, that's exactly how many they had burned out.
Technically, only 4 crystals has burned out. There were an unknown number of bypass circuits with a minimum of 2 but why not 4 for a total of 8 circuits for full redundancy?
This might also explain the reference in "Cats Paw" to channeling "bypass power" which suggests a separate power source rather than just a bypass around one?
In the episode the Enterprise was getting heated up externally and Kirk tells DeSalle to send bypass power to the heat dissipation units. It sounds like they're dumping excess energy from the main reactor around the crystal circuits for additional heat dissipation capability. Which oddly seems consistent with other bypass attempts from "The Return of the Archons" and "Arena" where they try to send power directly to the engines...
DESALLE: The temperature, sir. It keeps rising. Reading, Mister.
CHEKOV: It's up sixty degrees in the past thirty seconds. We're burning up, sir.
KIRK: DeSalle, channel bypass power into your heat dissipation units.
DESALLE: We've already done it, Captain. It had no effect. We're cooking up here.
Do we need a Trek Tech thread on the uses of Dilithium crystals by era?
Sure!
TOS: Crystals act like super capacitors and are able to be charged up with energy and discharge energy. Part of a crystal circuit in the crystal converter assembly. Also used for detecting antimatter phenomena. The Enterprise uses 4 crystals for full power utilization. They are not used to regulate M/AM reaction.
TOS Movies: They appear to be a Giant Crystal (compare to the smaller fist-sized TOS crystals or largish paddles) but do not regulate M/AM reaction. They appear to be necessary for energy storage and utilization.
TNG: A Giant Crystal (compare to the smaller fist-sized TOS crystals or largish paddles) regulate M/AM reaction in the warp core. It is necessary for M/AM reaction and to generate warp plasma.