Yeah, I seem to recall at least some non-canon sources referring to the Enterprise-class refit.
I think FASA originally came up with that terminology for their RPG, in which the Enterprise was the only one of the original Constitutions to survive its missions intact and Scotty's ideas for refitting and improving the ship after five years required more extensive modifications than originally thought. Hence why the ship wound up looking so different in TMP. The actual FASA rosters are a little hazier, as more than a few names were copied directly from the Constitution list to the Enterprise list without a "II" designation (USS Eagle II, for example; only the Enterprise would have been allowed letters) to suggest they were newer builds carrying the older names.
FWIW, in the TMP blueprints from Pocket Books, that Gene Roddenberry signed off on, the specs on the refit Enterprise
Type: HEAVY CRUISER
Class: STARSHIP II
Rather than settling anything, IMO this really supports all three competing interpretations of "Starship Class", Jein's, and FJ's. Since "MK IX" comes from the Space Seed
], these specs give weight to that graphic. Maybe TPTB decided to try to make all the fans happy with the TMP blueprints?