Short on time, as usual, forgive the brevity.
Shirt-sleeve environment in "Main Engineering".
"Work" on the "warp pods" in Jefferies Tube like arrangement.
Dilithium crystals are taken by hand out of various "boxes" in various locations, sometimes not in Main Engineering.
No large room-like sealed off "reactor" in Main Engineering.
Main Engineering is a relatively small room (in relation to the ship).
Radiation suits are the standard duty uniform in Main Engineering.
"Work" on the "M/AM core" is done in Main Engineering.
Dilithium crystals are presumably in Main Engineering (possibly in the 'Spock debraider').
Main Engineering is now a gigantic room spanning the dorsal of the secondary hull and presumably extending up into the warp engines.
The "intermix shafts" seen in ST movies are meant to move warp plasma around (to the engines, to the deflection crystal in the new impulse engines, to the phasers) they are not necessarily a TNG type warp core, though they look like one.
The closest thing to a warp core seems to be a small lucite room with airgaps around its revolving door.
Assume for the moment that TOS reactors are in the nacelles (aviation model). In the TMP upgrade they are removed to make room for additional equipment or in resizing the nacelles, moved to the secondary hull (more typical vehicle model), which now becomes a radiation sauna with the upgraded reactor at full capacity or damaged.
Why would they do this? Possible explanations:
Nacelle redesign required it (M/AM core effecting warp performance when in the nacelle itself, more warp coils, whatever).
Moving the reactor into the ship itself better protects the reactor (didn't seem to work out that way though).
Moving the reactor into the ship itself allows it to be worked on without entering the nacelles or going EVA.
Radiation suit company bought off a lot of Starfleet's top engineers.