You did very very good! You stayed calm, and kept explaining to her. Not that that helps, because she is not listening, but at least that's what other parents expect you to do because all the books tell us to do so.
To me it sounds you did everything pretty much as a perfect mother. And it's not working at this point. My oldest is the same. My experience? Reasoning doesn't help at this point. Just pick her up and leave as soon as possible when you feel she is going to throw a tantrum. After explaining once, skip the explaining, it makes you frustrated because she is at that point not able to listen and to correct her behavior once she has started it. She is stuck in the tantrum mode, and nothing helps. But I know, that's not what the books tell you.
I always talked with him afterwards, when he was calm.
The tantrums come and go in waves with my son. For months they're gone, and than we have some horrible weeks/days. He's now 4,5 and he has them less and less. So: one full year to go for you! just kidding, every child is different.
What helps by my second one (2,5 y) is counting. I show him 5 fingers and tell him: 5 more minutes. After 20 sec I show him 4 fingers and tell him: 4 more minutes. After 20 sec I show him 3 fingers .... That works for him. But it didn't work for my oldest. You can try.