Call the ATF and they will likely send you your money and then some and have you send the gun to an undisclosed address in Mexico.
In all seriousness, the local PD is not a bad option. your state may have laws against possesion of stolen firearms, regardless of what the DOJ or other TLA agency might think. better off coming clean and losing 500$ than losing your rights as a gun owner.
In preperation for the future please be prepared to be waitlisted by the FBI on all future background checks. you'll likely have a flag moving forward at no fault of your own it sounds.
Best of luck to you man and let us know how it turns out.
