(I didn't read the whole thread, so I hope this hasn't been mentioned already)
There's a tea shop I visit every time I'm in a particular tourist trap that I think offers tea sampling. They've got kettles and all the accouterments, but they don't really announce it when you walk in the store. I've only been there three times and the only time I was offered a taste of tea was when I asked for matcha and they only had it in wholesale amounts. I'm really unsure if it was a sample or if I'd have to pay (that may be my fault, I was feeling a little nervous that I'd say something that would expose how little I know about tea) So, I think you need to put it out there that the tea is free (if you had a little blackboard with the teas offered that day that also said free samples somewhere, that would solve it).
I also think that for shy-types such as myself you might also make it apparent that you're not going to be to put-out if I don't buy whatever tea I've tried and show me that it's no trouble to make me a cup. I know I'm defeating the purpose of the free sample a little bit, but if I feel like it's going to be a lot of trouble and I might not purchase it, I'm afraid to ask.
I also don't like to eat in front of people if I'm the only one eating/drinking. I doubt there's really anything you can do about that though, except if you allowed the employees to drink tea on the job.
Also, I really like this free sample idea. As a customer seeing and smelling this new and different teas would draw my attention to teas I might otherwise have never tried. It sounds so much more inviting than just rows and rows of tea. Too bad I'm probably nowhere near your store.