"Refit" is perfectly applicable.
My bad, it was, in fact, this very thread. Things move fast.
Well, not exactly.
Scotty says they've been "redesigning and refitting the Enterprise," and the alien ensign refers to Decker being on the ship "for every minute of her refitting" (in the Director's Cut and SLV). That's twice, not very specific to which part of the work it refers to, and every other use of the term "refit" in canon Trek has been consistent with the real-world meaning of the term and not the definition of "total reconstruction into a radically different design" that it picked up in fanon and ancillary materials.*
The movie itself refers to what happened as a "redesign" more often, with Scotty's line above, plus Decker twice calling it "the Enterprise/ship's redesign" when explaining why the phasers were broken in Kirk's quarters. That likely would've been the more correct name to give it, but "refit" is a shorter, punchier word to say, so that's probably why it won out.
*Thanks to chakoteya.net for letting me say that so authoritatively with so little actual research.