Econdude in Hillsboro, Oregon said: How can I overcome this barrier? Do you just have to get lucky and get with a firm and hope they ask you to manage projects so you can get your hours in?
If you actually have what it takes to be a PM, "luck" will not figure into the equation.
In most cases, there will be no hand-holding. When things go wrong, the project manager gets the blame. Oftentimes rightfully so. No one will listen to excuses.
If you are tougher than nails, can be very persuasive, prove that you can deliver results, and be willing to wear a target on your back 24x7, then I wish you godspeed.
I suggest studying the PMBOK. Your first "project" can be outlining a plan to get yourself hired at a growing firm that needs someone like you. Trust me, there will be projects no one else in the trenches wants to touch.