Ideally, when you go get Peachy's breakfast/snacks/etc, you'll want to wait until after she's stopped screaming (even for just a moment) or makes an acceptable contact call before going to her and giving her food and attention. What you did today is about on track, and yes - waiting until she makes her "pretty bird" call, responding, and then going to her with a treat/attention is the gist of it!
I used to struggle a lot with this same behaviour in Monty. Even now nearly 6 years in we have days where she seems to "revert" and have a really hard time id i leave her sight - specifically if i leave her and she hears me talking to people. How rude of me! It isn't perfect, but what'a more or less working right now is giving her a snack before I leave the room and a promise that I'll be back (i have a stash of nuts and nutriberries for this purpose), and if I'm leaving the house she wants me to turn on her radio and watch me get ready. When she finishes her snack, She'll usually contact call ("hello?"), and ill call back and tell her what im doing. Sometimes She'll escalate into screaming, but a lot of the time she's content with knowing where I am. If she's getting worked up past the point where She'll listen to reason, I bust out the "mom voice" and start counting to three. Monty usually snaps out of it and goes back to contact calling by the time I get to two, but if she isn't having it (usually if there're people and she can hear them talking, but can't see them) she gets a brief time out (in cage with cover on) lasting no more than 5 minutes.
The key is consistency. If you give in once, you've lost your progress!
Good luck with Peachy, and keep us posted.