I *think* this is how we did the door prize table last year:

Bring a garden-related prize worth right around $10 (so that no one brings a $40 item & goes home with a $2 item!).

When you bring your gift, you draw a "list number" out of a hat.

This number gives you your place on a list.

At the end of the swap, each person comes forward in numerical order to choose a gift.