I haven't read many TREK novels. If I'm remembering correctly, one novel explained warp drive as hyperspatial jumps. A ship would jump, take location readings, then jump again. One risked getting lost by jumping too far, so long voyages could be tedious. Along came Daystrom's new computers, which could take readings and plot a new course in the blink of an eye. Thus, the jump-jump-jump discontinuity of a starship seems fluid. The pseudo-movement bothers some people new to starflight the way the flicker of fluorescent lighting annoys some people today. At least, that's the way one novel explained it.
I think you're thinking of Diane Carey's Final Frontier
which featured Captain Robert April. I can't reconcile the events in it with what we got onscreen, but it was a fun read.
I think the one thing that is bit stale with the standardization of technology in Trek is that warp drive is the de facto FTL drive post-TOS.
If they didn't have FTL impulse engines, how would the Enterprise successfully evade the Doomsday Machine in "The Doomsday Machine" or only be years away from Earth bases (but not decades) in "WNMHGB" with her impulse engines? Or how about the impulse powered Romulan ship from "Balance of Terror"?
Do FTL drives from alien races like the "Total Conversion Drive" and "Ion Drive" now be classified as slower-than-light only because they don't have warp in the name?
Agreed. Once again it's too cute, neat and tidy.
BTW in WNMHGB Kirk says the bases were "days away but now years in the distance" because the warp drive is inoperative and they were now crawling at impulse.