I think the coils and energizers don't evaporate the plasma but simply suck all the energy out and then the plasma changes its aggregate phase back to deuterium gas. It is then pumped to the deuterium tanks or the reactors again.
Hm, that's an interesting notion. I would wonder, though, whether this waste plasma would actually be reusable, though? Still it's an interesting thought, and rather pleasing to think of the ship as a mostly closed system (minus the antimatter.) Are there any major instances of ships running out of deuterium? I can't recall any off-hand.
The ship would eventually run out of deuterium (and this happened in Voyager at least one time), because not all of it can be reused. My thinking is that the mixing ratio of matter and antimatter in the reactor is not 1:1. There is more deuterium pumped in, and that will absorb the energy from the reaction and become the highly energetic plasma. This plasma, after the energy has been "sucked" out by warp coils and energizers can then be reused as deuterium fuel.
However, a part of the deuterium (maybe most of it) used in the reactors will have been annihilated with antimatter and therefore is gone.
At the size I rendered it, each deck is 25 pixels tall and the ship is overall 4,934 pixels long. Three distinct possibilities:
(1) 10 ft decks:
10 ft/25 px: .4 ft/px
4934 px * .4 = 1973.6 ft = 601.55328/602 meters
(2) 12 ft decks:
12 ft/25 px = .48ft/px
4934 px * .48 = 2368.32 = 752.343936 meters
(3) 8 ft decks:
8 ft/25 px = .32 ft/px
4934 px * .32 = 1578.88 ft = 481.24624 meters
I'm leaning towards option one.
I agree on the 601 metres, but it's interesting that with option 3 we would roughly be at the "canon" length.