Keep in mind that for TOS that impulse engines have been implied to be capable of FTL. That's how the SS Valiant got out to edge of the galaxy in "Where No Man Has Gone Before" and how also the Enterprise got around when her warp drive was burnt out or damaged...
Wait, what? SS Valiant had warp drive. At least, they never said that it didn't have warp drive.
Also, there's room for the Enterprise to have remained at warp speeds after contact with the barrier and then having the crystals fail. After all, there's a fade to black and commercial break before the Captains Log...
"If you need a holodeck to make an interstellar starship on the bleeding edge of the unknown
interesting, something is seriously amiss."
- Straczynski & Zabel