Yes, your initial idea is correct. Put a prime in the front and then forget about the skid patches. However, as I said, you don't need that many unless you skid perfectly locked every time. For example, if you back pedal at all to slow down faster when you skid, you're spinning the tire through a much larger area than just the initial skid patch, so at some point your patches all overlap. It's been estimated that this happens around 8 or 9, but your mileage may vary.

In any case, if you're changing your cog all the time, go for a prime in the front. Otherwise, search for "odd number chainring" or read Sheldon's page about the possible benefits of even numbers of teeth. It doesn't take much to figure out skid patches, so there really isn't much benefit of a "set it and forget it" arrangement based on skid patches.