What they really should do is either can this Starfleet Academy, or "Flash/Blue Beetle" release it and then put Star Trek to bed for 4-5 years ("how can you miss me if I don't go away?" as the man in my avatar always said was used in the days of wrestling territories, and in comics to build up anticipation for a character coming back).
Come back in like 2029 or 2030 and have it be about the adventures of the NCC-1701-I, skip #NotMyEnterprise-G and one other starship, and set it like 50-60 years in the future. The G and H don't have to be referenced much other than a statue in a ready room or destroyed or have some over dramatic nonsense, both served long and productive times and were retired.
Fresh start. Keep the nostalgia and previous series references to a minimum or in a similar fashion to the first few years of TNG, and since this is going to be a massive Enterprise bigger than the F, a lot of the CGI can be used to make the ship appear massive or episodes not only about exploration, but the characters aboard this massive structure.