I see a lot of red flags, and I am not sure how aware H is, but he is setting you up to fail. I don't think this is fair to you. Putting a timeline on relationships, closeness, and love, is a double-edged sword! The timeline alone creates anxiety, which will not achieve intimacy. It will have the opposite effect. I am getting the sense that he has already checked out and this date he has given you is just his proof of due diligence, as if by giving the R "time," he has given it a chance.
It is a difficult dance to remain cordial, however creating space simultaneously. That is why focusing on you & GAL is the way to go. Let him see a woman only a fool would leave. Continue to be respectful and validate, however do not pursue him in any way. I wouldn't want him to think he has all the power--he can make choices about IF he will work on things and you are going to sit back and wait for that? No way.
He has you blaming yourself and feeling as if because you were not sexual enough, he may just decide to walk out in a few months. It is always two people in a relationship and perhaps he could have also been doing more to create intimacy and closeness so that you had more desire for sex.
Maybe H needs to see what he is deciding to give up--or will decide on August 1. A fabulous and sexy woman who is also the mother of his children. Sorry, but right now hubby gets a big thumbs down from me. You don't have to walk on eggshells for him. You just be fabulous for YOU.
“Forgiveness liberates the soul. It removes fear. That is why it is such a powerful weapon.” – Nelson Mandela