See, to me, fandom is easily more accepting of other ships, because of Voyager and Deep Space 9, and to a lesser extent the Excelsior, Titan, Excalibur and numerous others that the expanded media have followed.
However, go outside of fandom and there's two shows that people talk about. TOS and TNG. I think you could get away from Enterprise but only if you had a Kirk as THE main character. You need one of the two, ideally I'd say both which is one thing I really like about David.Blue's idea. Especially as Kirk's a she and not the captain.
The problem is the vast majority of the general people(this being the people who don't regularly follow Trek) have no idea what Excelsior, Titan and Excalibur are and only a few of the older ones may vaguely recall DS9 or Voyager as one of those other Star Trek shows.
To get the non-fans even remotely interested in watching you have to give them something they can relate with.