You say "I would prefer to be in the creating and fleshing out of ideas and stories, as well as managing the project," but those are two very different things.
My game dev experience (admittedly a little dated now - several different studios between 2002 and 2005) was that project management was completely separate from game design (the "fleshing out of ideas and stories").
The project manager took care of schedule tracking, coordinating people whose work relied on each other, ensuring that milestones were met and builds made and tested, keeping an eye on the bug backlog, etc.
The game designers were the guys in charge of ideas, story, gameplay design, etc.
If you don't have any games industry experience, but have solid project management experience in other fields of software development (preferably high pressure, large team, tight budget), I would attempt to parlay that into applying for a project management job.
Game design, though.. that's the tough one. Virtually everyone who has ever played a game fancies that they have great ideas and stories. Ideas are a dime a dozen, because the truly valuable ideas are one in a million. I would say that it is almost impossible to get a game design job from outside the industry with zero experience.
The roads in are: fund and start your own studio (I worked with a guy who did that - it didn't end well), or produce indie games impressive enough to catch the eye. The problem with the latter route is that if you're not a developer, you'd need to hook up with one to get your ideas made into an indie game, and once again, ideas are a dime a dozen and most of the indie game developers have their own ideas that they want to implement.