"I'd love to see a fan film that is set in the TOS era, with a non-Enterprise crew, on a different ship, with minimal (if any) crossovers, mentions of characters we've seen before, etc. that is simply just a standalone film and not written, produced or released as a precursor to a series."
I'm not sure TOS stories like that lend themselves to one-offs. They will just feel like isolated episodes as part of a series. So how can they be anything other than "precursors to a series"? And isn't it reasonable that when people successfully get the sets and costumes and crew together that they will want to do more than one story rather than just one and call it a day? That they rarely get that far doesn't change the fact that their intentions are reasonable.
It seems to me that Ajax will wind up fitting the bill for you, though, when it gets going soon, even though it is a series. Farragut has crossovers with the Enterprise (well, at least one).