Also, the FASA Star Trek IV Sourcebook Update likewise postulated a new-build NCC-1701-A, originally designated USS Atlantis (NCC-1786), and rechristened USS Enterprise after the Whalesong Crisis was resolved.
That said, I think authorial intent still has to be taken somewhat into account, with regard to the "new" Enterprise referenced in TFF -- it's very likely that William Shatner, Harve Bennett, and David Loughery were insinuating that the 1701-A was indeed a brand-new ship with Scotty's dialogue in that scene, and were intending for the audience to interpret it in that particular light, based on the rather simple and straightforward phrasing.
Again, true, that's by no means absolute proof, but it's worth considering, given the structure of the dialogue.