I was in same situation. In the end, three of my five references were PEs:
(1) By a stroke of luck, I changed jobs and my new manager was a PE. He did some consulting to industry, which probably didn't require a license, but got it anyway. So don't automatically assume no one in your organization is a PE. Put out the word that you're looking.
(2) I was getting my master's in management science at U. Mass Lowell, a program that blended technology development, manufacturing, and business. One of my electives was a design project with an engineering professor who had his PE license, as do many who consult (we also got a published paper out of the arrangement).
Your alma mater or current school (if you're continuing your education) are obvious choices. But also check out the faculty of community, technical, and small local colleges. Adjunct professors of math and science are often engineers moonlighting, and some of those are also consultants with their PE.
(3) My third reference was a consultant who had worked with a manager at a later job.
In all cases, you need to develop a relationship that allows the other to honestly judge your work as an engineer.
Since getting my PE, I've only run into one other PE in the wild west of industry, and he worked for a contract product development & manufacturing company. I make it known that I'm a PE, enourage young coworkers to at least start the process (the FE is easiest to pass when it's fresh), and tell them I'd be happy to give them a reference. None have followed up.
I wouldn't let the board disuade you from applying to sit for the exam, even if you don't have the necessary PE references. They may allow it but not want to go on the record.
Good luck.
Rob
Rob Campbell, PE