I finally was able to talk to Landlady tonight and she asked me to give her a bit more time.
We agreed that since this was not proper notice, I would pay for July I would move out on July 15.
If she found someone earlier than the end of the month, that she would refund me the last half of July's rent.
The irony is that if I had told her/made a decision when I was considering it the end of May, I would not be paying one more month of rent.
I do not regret it, I am who I am, and honour must be satisfied.