Several things apply.
Your original job offer was illegal and your boss knew it. The Bacon-Davis Act requires the prevailing union wage be posted so you know what is, by law, going to be paid.
You did accept what was offered. While living in your parents house you could afford to work for that money. The idea of the law was to lift workers from that level to paying mortgages on houses and participating in the economy.
There is a concept known as statute of limitations. You need to discover this. IF that time allowed for bringing suit has passed nothing can be done about your money. Too much time has passed...witness can't be found, evidence is lost.
The lawyer may already know this. Do not pay him in advance! He could legally ask for 1/3 of any award...and you would get something. If the statute of limitations has lapsed you get nothing but he keeps what you paid him.
Then there is your current...and earliest boss. You get to decide how much he owes you. If he has brought your wages along as your skills have increased that is one thing. If he is just keeping all the money as he continues to bid government work that is another.
See what you can discover from the contracting officer where you did the work independently of the lawyer.
Good luck,
Joe