I agree - getting the "mains" online is indeed the focus of the plot, but the way that is achieved by the crew is not done by messing with the "mains" directly.It's not the dialogue, it's the plot. They can't escape at warp without the mains being online. That's the whole reason Spock sacrifices his life -- because they have to get the warp drive up before Genesis blows and he doesn't have time to put on a radiation suit. So it is the single most integral plot point of the sequence that the mains being offline = no warp drive.
Partial main power is restored just before they set off for the nebula but the ship is still limited to STL speeds. Following the first exchange inside the nebula Scotty has to take "the mains" offline, yet retains propulsion and fully functional weapons. Whatever "partial mains" power was sustaining, it doesn't seem to have been either of those systems.
Maybe "partial main" power allowed the nacelles to generate the subspace mass reduction field that is so vital in allowing Impulse Engines to achieve 0.25 lightspeed? Certainly, without the "mains" the Enterprise was crawling away from the Reliant at a mere 6,800 KMH. I don't think that the Mutara nebula is literally next door to Regula and so the journey would have to have been made at an appreciable percentage of lightspeed.
If those "auxiliary" systems are the SIF or inertial dampeners, going to warp without them would be suicide!It can't be handwaved as an auxiliary system.

In fact, it's probably an inbuilt safety feature that having the dilithium power converters offline automatically trips off the warp drive circuits - thus explaining why the "mains" are offline and the best Scotty can do is rig a partial bypass to generate a subspace field.
Once Spock fixes the dilithium circuits, main power is automatically restored.