I figure that the thing on the floor in engineering in TOS was the reactor. We've seen it house the dilithium in "Elaan of Troyus." It is located at the rear of the saucer section. the two large round things are the mattar and anti-matter injectors. Tmatter and anti-matter are drawn up fromtheir storage areas inthe secondary hull. They are sent through the intermix chamber and then the drive plasma is sent back down to the engineering hull. The whole thing would occupy the same space as seen in TMP…
This sounds convoluted, but bizarrely it’s almost exactly the solution I arrived when I first drew up my own TOS deck plans back in college. My aim was to construct them relying SOLELY on the on-screen evidence, and they went together surprisingly well! I still have them somewhere if anyone’s interested in seeing scans.