If you have proof that Labor Ready agreed to pay you prevailing wage for the day, you can attempt to file a claim against them in small claims court. If it is a willful violation of the wage statute, you can request to be awarded three times the amount they actually owe you as damages pursuant to the statute. Small claims court is for disputes in amounts of up to 5000 dollars, and you cannot usually have an attorney represent you there. Good luck.
This answer is for general information purposes only and does not form an attorney-client relationship.
It is difficult to determine exactly what is occurring. Is this a problem on Labor Ready's end or the crew working the project? Is the public works crew reporting a higher rate, charging the state, then only paying you and Labor Ready a small portion? There are many problems with this scenario as you pointed out, I just don't know who to point fingers at.
There is a complaint process. I would encourage you to review the information at: http://www.lni.wa.gov/TradesLicensing/PrevWage/WageRates/WageComplaint/default.asp
lf you still have questions regarding your pay, and you have not received it, you should contact an attorney familiar with prevailing wage issues.