Becoming professor and showing autonomy - when to exclude supervising professor from co-authorship
Assuming that I understand it now, I do have a suggestion. Given the norms in your field, in which the PI is (I think) a co-author of every paper and who controls the grant and the research, you can't really distinguish yourself without help. But if others speak to your qualities more than you do, it might be enough - or even better. That would be the case in the US, anyway. Especially if that other is your PI and former advisor. You are, after all, his academic descendant. 

Suppose you are looking for a position elsewhere. Suppose your professor writes the letter that says you wrote the grant and were the lead investigator for much of what grew out of the grant. Not your words, but theirs. That is pretty strong. 

That may be easier to negotiate than trying to write as sole author, acknowledging the professor. Such might be possible, depending on personalities and norms, but maybe not. 

At the opposite extreme is excluding your professor unilaterally. I'm guessing that would be breaking norms in your field and place. It is also a terrible way to move forward if you become alienated from that professor. They are not going to be there for you either in career moves or research opportunities. 

In any case, it would be useful to have a conversation (or series of conversations) with your professor about this very question. "How can I distinguish myself here sufficiently so that I can move to an independent position? Can you help me do that? What should we do to enable it?" If the professor is honorable, and you don't suggest otherwise, you should get the help you need. And the professor, knowing the entire story may have options for you that none of us here can conceive of.