My bad on the TOS shuttles - I had completely forgotten about the instances where they had to be going at warp. Still, it's interesting that in "The Galileo Seven" they talk about the ion boosters and we see the exhaust coming out of the pods. I guess this isn't an out for the "simple impulse" line after all.
So we seem to be left with the bird-of-prey with apparent warp engines, like the shuttle, somehow being able to travel faster than light, and yet Scotty observing "their power is simple impulse."
To me, the only way to resolve this is the notion of some kind of revised definition of impulse drive, as others have suggested. Perhaps by the 24th, or even late 23rd, century, the term's use had been somewhat erroneously simplified down to "sublight propulsion," whereas previously it could refer to an alternate power source for both warp and sublight engines. I believe zDarby
was the first to float this notion.