Well, you could ship the extra chicks to your state agriculture committees in your legislature along with a note about how you don't want to have to buy 6 chicks... and ask them to change the law. If a few arrived dead perhaps it would highlight why it is a stupid law. (Not seriously...
1. Pay cash.
2. Shop at the local store where they don't ask for personal info, and where they don't make up policies and call them state law.
My Agway has the same problem with making up a 6-chick "law" - 'tain't the law folks. It's your store policy. I'm shopping elsewhere. That's my policy.