Jim, what about proofs with small non-intrusive name with copyright and date on the proof and on the back print out a small legal statement. I know it would entail double printing but might scare off a few of the thieves.
Alternatively: enclosing a small printed legal statement about not using proofs for reproduction and violators will be prosecuted. This shouldn't take much extra time or resources.

Anything you do will probably take some extra work and expense. I really have no foolproof suggestions for you. Even taking violators to small claims court is a big hassle and loss of time and money.

I hope you can figure something out to stop this problem