Becky, Sorry I can't remember exactly how old Henry is but I thought I'd share the way I encourage Stan to taste new foods, in case it helps. We always follow the exact same sequence of steps, and I go nuts with praise if he gets to the last step. He only gets his dessert (fruit or yoghurt) if he has tasted each different food on his plate.
We each have some of the new (or currently being rejected) food on our own plate, and we both do the steps together.
Step one is pick up a small piece of food in your fingers and I say if it is hot, cold, squashy, crunchy etc.
Step two is kiss the food
Step three is to stick your tongue out and touch the piece of food to your tongue a few times
Step four is to put it in your mouth and take it out again, in and out, in and out.
Step five is to bite and chew the piece of food.
This sequence works really well for us, having been doing it for a while Stan now knows all the steps and can do them by himself if he is feeling unsure about a particular food. He will often get to step 5, bite, chew and swallow the new food, and then repeat all the steps again. I talk to him about different textures and tastes as we are eating, to try and make them a positive thing. If he has tasted a new food and doesn't like it (or, bizarrely, says he likes it but says he doesn't want to eat it), that is fine.
Keep in mind that you may need to offer a new food 10-20 times before it enters his repetoire of accepted foods. So even if he refuses to taste it, still offer it again (this is particularly true for the staples that you frequently eat in your house). The other thing I try to do is, if he eats a new food, to serve it again very soon after, and again soon after that, to try to 'cement' his familiarity and enjoyment of it.