If the answer is yes I would suggest:
- do some serious homework about what this new proj entails; come up with some concrete points why you can lead it.
- ask nicely to meet with H one-on-one; let him know why you believe you can do the job particularly with his help, which would free him up for other respon*****ilities. Tell him you really count on his support to learn more and contribute more to the group.
- Tell H you are thinking about talking to Y and ask if he would be nice enough to join you in the conversation.
- Meet with both of them and talk nicely about why you would like to contribute more by taking the lead role.
BTW, I like the way you handled H so far by not go head to head with him. If there is no chance of rotation/transfer, I'd say use his own way back to him - 隨時都笑樣 on the surface when you deal with him. But push back gently when he steps over the boundary.