Welcome to FT, zem52887!
I personally feel you're missing a great opportunity by avoiding TK and IST, but that's a personal decision.
You're just going to have to keep looking every day to see if availability opens up. It can happen any time. If you're unlucky, it won't happen, but September isn't prime travel time, so I think you have a decent chance.
You may also want to book a less-than-ideal routing as a backup.