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Depending on the size of your mule you may want to consider investing in a towed cultipacker to keep the roadbed in line and compacted. It works very well after a rain just like a sheeps foot roller.
If you can find a used single wing cultipacker or take a used double winged one and simply take one side off the wing can remain folded over the center section and the added weight will pack the dirt and stones down very well.
But If you have a row crop mule there is no need to remove a wing as the mule will be able to tow it with no issues.
It would be less work if you rented a small vibrating double drum roller for a day as it would work even better.
If you do not have good drainage meaning a crown in the center of the driveway to allow drainage a small vibrating roller is the best way to do this.