My method is a little riskier than that, but you can do it any time.
Go into the parking garage, and do things that'll start raising your police record. You know, blow up cars, snipe pedestrians, block traffic with your car and toss a grenade at the pileup, that sort of thing. Once you get up to three stars, rocketing helicopters will ensure a swift ride up to five.
Get in a car (whatever you can find -- a taxi will be fine), and drive through the first-floor entrance closest to the alley leading to the Pay & Spray. Hang a right, and an immediate right down that alley. Don't go full speed; you want at least one FBI car to follow you. Lead it up the ramp and to the Pay & Spray; when they're close, dive into the Pay & Spray to clean your record.
When you exit, the FBI car should still be there. Steal it; it'll probably give you an immediate star or two, but drive IT straight into the Pay & Spray. (Yes, you can spray an FBI car; it's the one law vehicle that you can do that with.) If agents are between you and the back wall of the P&S garage, run over them for the humor value. Repeat until the vehicle is yours and your record is clean, then drive it to your garage and save it. Then, off to the crane!
I am distracted right now, because I downloaded DAPHNE (the laserdisc emulator) and the Cliff Hanger MPEG-2 footage. I haven't played this game in fifteen years, and I doubt I'll get any sleep tonight.
