Here's an idea. How about they move forward from the stone age, and utilize a little technology? Treat it like a business. Only government could run something so poorly, and stay afloat.
1) Submit your prints once, keep them on file for future use.
2) Submit forms online. Surely someone could make a program that could run your information and background check.
3) Pay with a credit card online as well.
Yeah, and it'll cost $250 million to develop and implement, over-run its budget by $100 million, take 10 years, and eventually be scrapped as a failure.