If you can still get the grey "Ozite" CRC carpet, it will save you some money over the black carpet. When it gets dirty, you just vacuum it. If the environment gets really dusty, perhaps some tarps will do the trick to reduce the amount of cleanup. If you are feeling energetic, you could always roll up the carpet and store it till ready to race again. That's what we had to do regularly at our local track as it was at a fairground facility to be used for events other than racing. Get a case of duct tape, carpet tape or Gaffers tape as you will need it each time the carpet is set up.
There are also low profile carpet tiles that may be good for a multipurpose flooring.
As mentioned, you can use an asphalt sealer and just wash it from time to time. the natural grip from the grit in the sealer will provide decent traction even without an additive.