I didn't do a big marketing push for itch.io, only social networking and no PR. I did it back in July 8, when the game was published on Steam, and didn't have the energy to go through that again for itch. Again, I didn't open this issue for myself, since its late for me, but for others coming behind me. Some of them will do marketing for their itch.io release regardless of whether their game has been released on other platforms before or not.
There is no exclusivity involved necessarily with PR (sometimes there is), but journalists who agree to cover your game (which is a very rare event for indies) expect that you tell them the release date and that you keep the promise, so what they publish are "fresh news". So if anyone writes an article saying "Game X is now available on itch.io", they don't want to look unprofessional in the eyes of their readers who know the game has been published for days or weeks already. That's why I mentioned that not knowing when the game is "fully published" makes PR really hard, or impossible.
Changing the status after review, as you suggest, is a good starting point. But how do I know when the review is completed?