It's a bit dubious whether the standard mode of TOS shuttle sublight propulsion would involve rockets at all. Chiefly, if the standard rocket flame is invisible, it would be quite difficult for Spock to make it visible without special preparations. "Dumping fuel into the flame" is fine and well as such, but as said, there is basically no fuel left for the trick... Will the tiny amount really make a difference?
Well perhaps fusion-powered rockets.
"Rockets" were referred to in "The Cage" for "blasting out" of orbit. In "The Naked Time", the impulse engines were called to "blast" them out of orbit.
Back to the shuttle in "Galileo 7". The phaser energy conversion must have been for creating new "fusion fuel" since at the time of lift off they had more then enough to make orbit by firing their boosters.
SPOCK: That is a most illogical attitude. Orbit in one minute, Mister Scott. Fuel status?
SCOTT: Fifteen pounds psi. Approximately enough for one orbit, sir.
MCCOY: After that?
SCOTT: Tapping our boosters ended our last chance for a soft landing.
IMO, it seems that the reactor is part of what feeds the engines with fuel which give the shuttle thrust. That mirrors the starship Enterprise's power setup with the big difference in that lithium/dilithium is not involved which gives them a limited fuel capacity.
Robert Comsol wrote:
Therefore b) and c) consume the fuel calculated necessary for the vessel to make it back to a rendezvous point with another Romulan vessel in Romulan territory.
The fuel consumed on the Romulan ship sounds more like it is used for generating power to it's other power consuming systems, such as the plasma weapon, propulsion and cloaking device. Based on the episode, propulsion uses the least amount of energy (aka fuel cost) while the cloak has its own energy / fuel cost and the plasma weapon takes all the energy briefly (and is the biggest fuel cost). Unlike the Enterprise's re-generating power systems, the Romulans have to be mindful of their fuel consumption which is like that of a TOS shuttlecraft operator.
Robert Comsol wrote:
I should add, that I'm a strong supporter that the Romulan ship according to Scotty indeed only has sublight impulse drive (before the vessels were retrofitted in "The Deadly Years" with true warp engines). That the vessel is about to pass a sublight speed comet's trail is a hint, IMHO.
Passing through a sublight-speed comet's trail doesn't indicate that they were at sublight. Ships at FTL do interact with things in "real space" in TOS - the Enterprise warps through the tail. And given how long it takes to warp through the tail, we can tell that it must be a rather large one with a large cross section.