A short story won't give you the room to work on "all the ideas in general." If you want to work on those ideas, the novel, floundering or not, is the place to do it. To lean on Stephen King, he's the one who said something like this: The more lost you feel, the faster you should write. The idea, of course, that by doing this, you will finish the story.
As to the matter of turning a novel into a short story, yes, did that. Wrote a SF novel that no one wanted, then sat down and wrote a short story version of it. Thing is, that short story had almost nothing in common with the novel, beyond its main idea. Good news, though, is that the short story turned out to be my first professional sale. (I have long since foolishly spent the money, which is the only way I know how to spend...)
So why was the short story so different from the novel? I tossed out everything but the central idea -- the big, "what is the story about?" engine that drove the thing -- then added a character with a problem similar to the one the main character had in the novel, kept the noire feel, wrapped it up in a veneer of social isolation and gloom, turned the crank, and got a short story about futuristic drug addiction, the kinds of people who engage in this particular vice, and what effect the abandonment of mere humanity might have.
In the end, the novel was about these things, too, but told from the perspective of a cop who had to do a bunch of things to stop the spread of the humanity-warping drug. The short story was told from the perspective of a petty crook/druggie who bungled a small-time deal with the antagonist from the novel and was left dealing with the consequences. Whereas the novel was about several events, the short story was really about only two, which were hope and betrayal.
Which reminds me: it was Philip K. Dick who once said that novels are about a series of events, short stories about one.
Maybe you could pick one of the events from your novel and turn it into a short story?