It's the same problem the social progressives (read: religious right) have been facing (and will increasingly face) with the Republicans.

The short answer is "No, if you want to avoid handing control to the Republicans, who are infinitely worse."

I think the best thing to do is brand yourself within the party and nibble away from the bottom up. The Tea Party did this to great effect, and shifted the Republican party even further to the right by knocking down more regional House slots. They still ran as Republicans but they were branded Republicans and the brand meant something.

It's worth keeping in mind that while the Tea Party succeeded in moving the Republicans to the right and not splintering the vote in the Dem's favor by going 3rd party in head to head races, their strategy still cost the Republicans dearly in some races. They are still grappling with the pros and cons of the swollen Tea Party ranks.

But it was the most effective branded ideological shift I've seen executed in my memory. They had a lot of billionaire and media help though. They weren't as grass roots as they claimed to be.

Edit: I once heard a Green Party candidate running for a local seat speak. I shit you not he worked himself into a frenzy and at one point started yelling "And we will rise up with our Green brothers and sisters in Germany and...." I mean, he lost me before that, but I was half expecting a Heil Hitler. I've seen many Greens reference Germany and it makes me infer that there must be a really strong Green party presence there. Makes me not even go near considering a domestic Green candidate. It's bad enough they are making a platform out of a single issue without forgetting who they are representing.