I realize this is tough, but you can't blame him for wanting his boys. No matter what, someone's children are more important in the long run. You won't give up your girls, would you? Once you have kids the rules change. I think it says good things about a man that thinks his kids come first, before himself. It doesn't make it easier for you. Here you have a guy trying to do what is right.
With a marriage that lasted 15 years, there are many ends to tie up properly, so that you could move on. If he is still going ahead with the divorce and it's as soon as 3 months, your best bet is to give him the space he needs. He may be trying to make things easier for the children and for himself. He might feel he has a better chance in court dealing with custody. He may feel that it's best not to stress them more than they are now. He needs timee to work this out for himself.
You don't have to give up, he may be back when the divorce is a done deal. Visitation is in writing and ordered by the court. He simple may be on overload with the thoughts of his children hurting so badly and the divorce. Seems all too possible that you might have to step back if you really want to be with him. Let him do it the way that he needs to, so that his heart is free to give to you.
I'm so sorry this seems like a rotten answer, but it's not. You may have found a man with heart and honor. He knows the value of a good family. He knows what it means to be there for his kids. He would be more likely to do the same for your girls if things work out. You want a future with this man, with your girls. He wants a future with his boys. I think it's a brave thing to sacrifice his wants and you to be the father he is.
Don't give up, just give it time and space. You've had a time when there was too much on your plate to sort it out. He's there right now. If you love him, you'll want his happiness too. Don't push, but support. He'll remember when it's done who was there for him.
I hope things go well. My best wishes to you.