Have you considered moving?

Thanks for your compliment.:-) You have very good observation and understanding of your current situation, only thing I tried to prvoide is a little inspiration to help you think more.
Now you must be thinking what you should do given the situation. it's clear to me that your goal is not to take back the project, but merely to be acknowledged by your contributition. It's a thinking of a team player and I would say that A was lucky to have you on the project. It could be a win-win situation for both him and you, but unfortunately he failed to see that. To be honest, I think that it's too late to reset the relation between you and A. I think that he will try to stick to the way it is now.
The reality at work is that if you failed in one place, it would take you extreme effort to turn things back, and sometimes it's just too hard for most people. Have you considered an internal transfer or even looking outside? I assume that you are working in a big cooperate. Since you have excellent technical skills, it should be easy for you to transfer. From my own experience, things always get better when you move as every time you move you have more experience than last time.