L.B.
Our daughter did that same thing! After trying the things you did, a Dr. recommended we "pop" her mouth...not a spanking, but a "pop" -- like if you wanted to make a pop sound with your mouth, you'd pop your lips. It doesn't hurt, but REALLY surprised her...to a point she'd grasp her breath, thus stopping the screech. As she'd breathe in, it gave us time to get right up in her face and say, "no"...firmly; not mad, just firm. It doesn't take long for this to be effective. The other thing the Dr. recommended was to put water on our fingers and flick it at her face. It would have the same effect -- make her gasp in surprise and give us time to get in her face and firmly say "no."
As she got older, she'd realize we wouldn't "pop" her in public, so she would pull this same thing when we were in public. At the state fair, (she was 3 at the time), we sat her on the curb and told her she was in "time out" until she could control herself. Then, my DH and I stood with our back to her (about a step in front) and let her scream it out. Yes, we got looks, but the second time we had to do that, the screaming was shorter...the third time we did it, shorter still. We sat on curbs by the sides of highways, outside of restaurants, outside grocery stores (I'd leave a full cart in an aisle sometimes to take her outside), etc. One day, just the threat of doing it was enough to stop her. Incidentally, when people would look at us disapprovingly, we'd ignore it. Many people would give us a "knowing" look like "I've been there, man, keep at it." Others would smile an encouraging smile. If you're a step away from someone making loud noise...even with your back turned, you are clearly in control.
Good luck!!