As far as TOS goes, I don't recall an instance where Kirk orders the ship to slow to impulse while in any storm. Even in an Ion Storm, he calls for Warp. But going back to the dialogue, Kirk doesn't say "If only they could use their warp drive in that storm" or something like that. That is only if you base your belief that impulse engines are sublight only. Perhaps in TNG and onwards it is, but that's another series and another production staff (Although IIRC, TNG goofed in Best of Both Worlds pt2 and had the E-D at impulse cross a distance in a timeframe too short to be sublight...) I'm afraid the dialogue supports 200 (or more years) not 170.