I've recently contracted one new client and started chatting with another potential - both are from my prenatal yoga class

The new client owns the shop where the classes are held, the other is a local business owner/restraunteur...both are fabulous women entrepreneurs!
We've also recently started chatting with our birthing class teacher. Her husband is a local and well established small design firm and he's curious about outsourcing some work to us....
Once people find out what you do - and this conversation can come up anywhere, anytime, it's not that hard to pique interest and slip in small ways you might help enhance their own business growth. The key is to keep it very low key, I think, so it doesn't feel sales-y to anyone. After all, in a social situation no one wants to be sold.
I don't see why you couldn't give your t-shirt idea a shot! I think it's a great way to invite people to approach you out of curiosity.
If you do end up having shirts made, let us know what comes of it!