A while back I came to the conclusion that the biggest reason SF is more or less off in its own ghetto of readers and producers is the same reason modern literary fiction has ended up in a similar cul-de-sac. The people responsible for it make you work so hard to be part of the club and to so little effect — albeit in different ways — that it's no wonder most people just give up and reach for the Dan Brown and the E.L. James. Readers have better things to do with their time than beat their heads against walls erected by the self-important. The hard part is not identifying this problem; it's doing something about it.
The only real answer may be in the form of individual pieces of work that strive as much as they can to not embody all the most overarching failures of their respective genres. I'm turned off by a lot of modern SF not because it's not SF (or even because it's SF) but because it's being written more and more in a self-sustaining vacuum. When it takes ideas from other literary paths, they're mostly stylistic rather than spiritual. Earlier SF is far more an influence on current SF than, say, The Grapes of Wrath or The Accidental Tourist are (that last book garnering my vote for the most unpretentiously successful work of literary fiction from that decade). The field is starving itself to death, but no one seems to be particularly worked up about it — or, rather, most of the responses to such a state of affairs involve borrowing all the wrong things from all the wrong places and calling that "innovation".
As an aside, I suspect a big part of why SF-ians wrinkle their lips whenever they hear the word "literary" is because so much of the way we teach literature and get people interested in it backfires horribly. It starts in high school, where we do dumb things like trying to get kids to read books that nine-tenths of them aren't going to connect with even on the most abstract levels (The Great Gatsby is a major victim of this kind of abuse), and it continues in college, where the recherche and the academically insular become values unto themselves to the detriment of just about everything else. We teach this stuff in all the wrong ways, and do terrible disservices to the folks who are drawn to it for real.
Small wonder few SF-ians want to go rummaging around in the literary toybox for anything inspirational: it's because they've been systematically taught to see the whole endeavor as a succession of bloodless academic exercises about people they wouldn't spend five minutes with doing things they can't make head or tail of. Instead of being thrown into the deep end of the canon pool and told to start swimming, they should be given tools by which to connect their own experiences back into the times and places of a book's genesis, and then work from there into the books themselves. A genre literature that's informed by literature generally, and life as a whole, makes everyone's reading experiences better.
But again, I'm reluctant to try and find a solution in the form of a movement, label, or plan, because that's how things become mere checklist-conformance exercises. A good piece of writing isn't good merely because it satisfies certain requirements for being placed on a certain shelf; it makes us say "Now why didn't we ever try anything like that before?". It's good because it makes us want to go back for more, at diferent stages in our lives, and see something new each time. And, maybe most importantly, it inspires us to do at least as well, if not better, in our own work. None of this can be contained within, or inspired by, a formula.
All of this, unfortunately, flies in the face of the way most books find an audience in the first place. I noted before how most people don't know how to spread the word about something that defies expectations, and the people who do know how to do such a thing generally have very little leverage over anyone outside of their own circle of friends. (Besides, everyone's a critic today, right?)
So while the first step is to write outside the box, there's others after that which have yet to be sussed out. But that first step is proving complex and nuanced enough to be fuel for a whole career by itself.