How am I supposed to discipline a 3yo who WANTS time out?

Timeouts have mostly worked for us, except for the biggest issue we’re dealing with, which is wanting my undivided attention.

I can’t take this girl anywhere where I might want/need to have an actual conversation with another adult. She screams and kicks and runs away. She BEGS for me to leave, even if I threaten her with timeouts. We both know they’re temporary. And nobody is even ABLE to sit with me through the screaming, because people have jobs and their own kids to worry about (my husband, who’s not as triggered by screaming as I am, often offers to sit with us and stands by my efforts to discipline her, he just can’t do it all the time because he has work).

Every form of advice is just about sitting with them and validating their emotions, which I understand, but I’m at a loss for how to enforce some kind of boundary in public.

The thing is she does comprehend social scripts pretty well. She doesn’t mind shopping or errands with light small talk, she had a blast trick-or-treating (right until a neighbor tried to chat with us past the exchange of candy). But if it’s an open-ended situation she panics and wants me to get us out of there.

Also I do talk to her about what she did after getting her from timeout, not mid-tantrum, and she just squirms and avoids me at best, tantrums again at worst. One weekend I just kept putting her back in timeout until she stopped ignoring me and said, out loud, “I’ll behave” (I gave her food and water during the ordeal). But even that was a specific action I asked her to take, not an inaction, if that makes sense.

I’m beginning to see glimmers of hope; she’s starting to say “be patient” to herself when she’s getting impatient, and she’s not upset when I leave the house anymore, because she knows I’m coming back. But today I just broke down crying because I’m not the patient zen master these parenting advice blogs seem to expect me to be. I have the hardest time self-regulating and it takes all my willpower to not scream and cry myself, let alone talk her down. Please help me.