Hi Matt,
I suggest to approach the problem from the mechanical side.
Police lights are normally filament type lamps with a rotating parabolic mirror to make them omnidirectional with a flashing effect. LEDs are directional components with a view angle of max 120 degrees (most LEDs up to 90 with rapidly decreasing light intensity at increasing view angle)
To compensate for that you might construct a rotating disc with the power LED (3 to 5W). The disc will have contactors at the bottom to allow for free rotation of the LED mounted on top.
Maybe in some places, but here in Florida, they switch to LEDs a few years ago, and very low profile. It's almost impossible to spot-the-cop, from the lights sticking up on the roof. They also drive several different makes/model cars, so you can't guess from that either. Haven't seen the rotating lights on a police car in many years, and fortunately not behind me...
I posted the news link, because there are many such light-bar projects here, and figured since it was recent, it would gives some of the people who stumble onto the thread something to think about. I made a little flashing tag for my dog, mostly because he's a black Labrador, very fast, and almost impossible to see at night. The local police weren't amused, just told me to remove it.
Anyway, the best route is using a microcontroller, a single chip for under a buck, transistor or fet to switch, and a buck-puck or similar driver for the high wattage LEDs. Don't forget the heatsinks. There quite a few current drivers for the LEDs, that you can build, but the cost difference isn't great enough for the added complexity. Not a real tough project, getting started with microcontrollers isn't as bad as it sounds, nor all that expensive, but well worth time and money you save, since your control circuit can be copied in minutes, and only one chip to install.