Certainly building movie-era sets that are as faithful as the sets that STC and STNV and Exeter created for the TOS era would be tremendously expensive. No one has done that.
Which doesn't rule out doing a convincing movie-era crossover. It would simply have to be written so that most of it takes place on locations other than the Starfleet ships.
NV did a great job of evoking the movie bridge design for the Excelsior in "World Enough And Time" - they built essential elements of the set for a couple of angles, shot it carefully and then enhanced it considerably with CG. With careful planning and effort STC and Farragut could do something similar for one or two important ship-bound scenes.
When Exeter was first being done ("The Savage Empire") and then a few years later Farragut produced "The Captaincy," I was struck that the economics of doing a fan film were about the reverse of doing a Trek series at Paramount: ie, it was cheaper and easier to shoot on location than to outfit a studio and build sets.