Well, strictly speaking for dramatic purposes there's no reason why the engine room couldn't simply be a control room tucked between the nacelle pylons next to a transformer or circuit breaker that brings ship's power down from the nacelles to the rest of the ship. In point of fact, most engineering decisions on modern naval vessels are made in the maneuver room or the motor room, not the room where the actual power plant (or reactor on a nuke boat) really are.
On the other hand, the same can be said for the TMP Enterprise. Arguably, the intermix chamber was just a power transfer conduit with the reactor room far below decks, so "Engine Room" in the refit Constitution refit could be anywhere you need it to be.
That gives me a thought. Suppose the warp reactors of the TOS ship really was in the engine nacelles? In that case the gigantic machinery bay on the other side of the chainlink fence might just be a massive energizer array where drive plasma is siphoned downwards from the warp nacelles and then converted into energy.
On the other hand, the same could be said for the TMP Enterprise. There's certainly nothing in canon that suggests the intermix chamber MUST feed towards the nacelles and not the other way around. It's entirely possible the drive plasma is produced in the warp nacelles (where the bussard collectors are) and channeled down to the so-called "Engine Room" where it's converted to electrical energy or channeled into the impulse engines high above or the main deflector far below.
The only thing that doesn't fit this theory is 24th century technology, but then there's no reason to assume the 24th century equivalent isn't vastly more advanced than the engine designs of a century earlier, appearances aside (like the difference between a piston-driven aircraft and its jet-powered counterpart).
The drive plasma is indeed created by the interaction of the matter-antimatter hitting the dilithium. It is then fed through the nacelles where it is accelerated in preperation for the nacelles (acclerated plasma has it's own gravitational turbulence, which would explain how the subspace fields semi-warp space.), then it interacts with the naclles materials to produce the warping subspace fields.
Since there is no canon explanation of how this happens, I came up with my own viable theory.
Perhaps Dilithium initially is just a form or variant of lithium. It's travelling through space on an asteroid or comet, and said asteroid or comet interacts with subspace in some way (a subspace pocket, a breach in subspace, etc.). Through that reaction, it changes the nature of said lithium creating dilithium. Then it hits a planet where it's mined. This would makes sense considering in TOS dilithium was a rare element.
Because it phases into subspace and is bombarded with intense radiation in the process, when antimatter and matter collides with it the the crystal phases out of space time and partially into subspace, which phases the created plasma as well, which makes it the perfect fuel to create subspace fields. That also explains why the crystal doesn't annhiliate when matter and antimatter hits the crystal.
Just a theory, but one that at least partially fits onscreen evidence.