I got so carried away waffling I didn't address your question about how I get out of a corner or bind in a story. I point you to
this thread that I posted some time ago. In that Susan Sontag offers the hint that the problem IS the solution.
This resonated with me because it is the way it seems to work for me (when I can make it work). Whenever I thought I was getting into something I couldn't get out of, it turned out that the problem itself was a significant part of the story. One big (for me) example: As I was writing the background story behind my series, I hit some difficulties with the way a character interacted with others; the character needed to keep a secret and I wasn't sure how. The solution to that, that a secret was possible, and the reason why it was possible, had implications that ran right through the background and to the end of the series. (I still remember where I was and what I was doing when this came to me, it was a very significant moment.)