Regardless what they do, they have a hard road ahead, being an asphalt track on an island in dirt country. Not sure that there even is an answer.
If it were me, I would travel to a few of the bigger asphalt super late races, and round up as many used tires as I could. The super late guys aren't going to run them more than once, but they still have life in them. We filled our box truck to the ceiling once after a race at Sandusky with what was left behind in the pits after the races, and raced the whole next season at Hickory on them. Bring back what you find and give them to guys to try their dirt cars on pavement. Small price to pay when your main objective is to try to get racers to your track.
Rules? Limit of four tires and one engine. Get any cars you can get and try to put on a show. Qualify everybody and run classes by brackets on how they time, and time the leader each lap on a breakout time to prevent sandbagging.
Payout? Give everybody the same amount, maybe a few bucks more to the winner, but you want any and all cars that you can get.