Hissy is giving you fantastic advice here Joblot.
Limbo land is lousy, the worse place to be. I was in it for a few weeks before ex left, and every day was like a week. I just got through it. I tried to gain all my strength and stay positive and kept focussing on the light at the end of the tunnel. You need a date or at least a small timescale for her to leave. September - well it could be the 1st or 30th! So try and make it clear when you want her out in September. Don't wait for her, but say something like, "I think it would be best if you could find somewhere by the 10th" sort of thing.
Then you'll be able to literally mark days off in your head. I got through it by keeping my distance as much as possible from ex, by being polite and civil when we were together, but not engaging in anything other than necessary talk. No small chat, jokes, "how are you?" kind of stuff. It is hard. I think that if you are sharing a bed, it's crucial that you stop. Even if this means that she won't leave the bed, and you sleep on the sofa/elsewhere. This will show her that you really mean business, and also give you space too. It's only for a few weeks. You don't have to be cruel - just resolute. She needs to see that this is for real, and that you won't respond to her jibes, insults, threats and tears. You can say stuff like, "I'm sorry we are going through this, I'm hurt too, but there's no turning back".
You are not responsible for this. You have every right to want out. It sounds like you've put up with far more than many people would. Which shows how much you wanted this to work. But in your heart of hearts you know it's over, and there's no solid foundations left to build a healthy future with her on.
So stay strong, lean on RL people, (and us) and build up a social life that's free from her. See other people as much as you can. Get away (even for a 20 minute walk) if you can.
You'll be ok. You just have a few weeks to get through.