Clay won't really take the swirl marks out of the paintwork, its mainly used to take the impurities out of the paint to give you a better finish when you wax and polish it. To get rid of them you may need to get a full paint correction done by a detailer or if you are confident enough then you could mop it yourself using the various compounds.
Your best idea initially would be to PM or email Tom at TK Detailing, he's one of the club sponsors, who will give you advice on how to remove them and or a price to detail the car for you. He did mine and the finish was awesome.
Failing that Poor Boys black hole glaze will help hide the swirls but wont get rid of them.