We're a day behind you, we arrive at CSA Sunday.
I don't think it's worth the private car, the shuttle is fine, and it's a good way to meet some other couples that will be at the resort.
Not unless you're a certified NASCAR or demolition derby driver! They drive on the "wrong" side of the road, by U.S. standards, and pretty radically-but it works well for them. Leave the driving to the Jamaican professionals!!
I would skip a private car. The shuttle is a nice experience! This will be our 3rd time back to CSA and we are actually looking into taking the Tim Air flight to the resort and take the shuttle back. Not sure yet though.