You don"t need a new starter. You just don"t want to run it for long periods of time trying to start the tractor. You"ll either need a real 12V coil (~3.2 ohms primary resistance)or you need to add a ballast resistor in series with the coil in the primary circuit with the existing6V coil(~1.6 ohms primary resistance).
Your call. Personally, I"d recommend getting the real 12V coil (NAPA Part # IC-14SB).