I had the exact same problem! I'm a Controls Engineer with over 20 years exerience. Until 5 years ago, I never worked with any PE's. I even tried doing some part time consulting for a PE and the NJ State Board reject that reference as acceptable supervision.
In NJ you need 5 references, 3 of which must be a PE, and one must be your direct supervisor. You may be able to get a couple of references by networking or joining a professional group, but until you have direct supervision of your engineering work for 4 years from a licensed PE it is going to be difficult to get permission to sit for the test.
One avenue to reduce the time needed of PE supervision is to get your Masters degree or Doctorate degree. Typically you get one year of credit for a Masters degree and two years of credit for a Doctorate degree.
I understand why the State Board does it like this, after all, would you want to drive across a bridge or drive thru a tunnel designed by some guy who sat for one 8 hour exam and happened to be a lucky guesser?!?! But with that being said...getting a PE license is kinda like joining a Fraternity, where you can't get in unless you know someone from that Fraternity!
Hang in there! It took me 19 years! But life has a way of sorting itself out...