First off, it's so encouraging to see how much you care about your boyfriend, even (and especially) when he is going through such a hard time with his anxiety disorder.
Similar to your boyfriend, I also struggle with anxiety, have expressed doubts about myself, and at times have not felt good enough for my girlfriend either.
I think what you have been doing so far sounds excellent, which is simply telling him that you'll be there for him no matter what and also by being open about your own insecurities. It's obvious that you really care about him just because you found this forum to open up about your situation.
In addition, my girlfriend has told me several times that in a long-term relationship, you should be able to go through the highest-highs and lowest-lows and make it out together. The most important thing to add to that, however, is that your boyfriend IS at least trying to make progress to heal from his anxiety (such as by using the materials from this program). You CAN'T heal your boyfriend yourself, you can only provide a place of love and acceptance. The fact that he is not communicating does not sound like a good sign, as he must be ruminating over his anxieties by himself.
When I was doing something similar, my girlfriend acted disappointed and upset that I would not share what was on my mind. She felt that I was "hiding" things from her. When I realized how important it was for me to talk with her about what is going on in my mind, regardless of how silly or sad it sounded to me at first, I started opening up to her more, and I think that also has brought us closer together. It has certainly helped me heal a lot, too.
Moreover, I hope that he will start opening up to you more about what he is going through. A lot of the negative beliefs he may have about himself right now because of his childhood are NOT true, and it will take some time for him to let go of those beliefs and form more rational ones. Like you said, he is loving, funny and intelligent - but the problem is that he does not believe that about himself right now. By slowly helping him come to believe those facts, his anxieties will have a lesser grip on him, and he will start to see the same great qualities in himself that you see.