Tantrums as you explain it can often be about something totally unrelated. My oldest son is like you describe and I find the only thing that he is able to understand is when I acknowledge his feelings. That's all he wants is to be heard and to feel like I understand him.
So when I ask him to get off the computer (for example) and he says no he wont and starts gearing up to FREAK OUT (I am sure you get the capital emphasis here
) then I go to him, hold him gently and lovingly and quietly look him in the eye and acknowledge his feelings. "I hear that you want to keep playing. I know that you love your game and you want to keep levelling up." Then I state the boundary "It's time to eat now. You had a lot of screen time today and your eyes need to rest so that they can play more tomorrow". Then I love him and show acceptance again of his feelings by granting his wish in fantasy: "I wish we could both sit and play on the computer all the time/all day/all night." Or "I bet when you are an adult you will eat while you play or just skip dinner and play all night long!".
If he still gets upset, I just love him through it as best I am able to at the time, but he always switches off then - even if he grumbles and moans throughout.
And sometimes when I set a specific boundary and the tantrum ensues, 90% of the time he will end up talking to me about something totally unrelated to the action that seemed to spark the tantrum! Maybe someone was mean earlier, maybe he feels out of control of his own life, or whatever. He just uses the opening for the tantrum when he spots it.
But you cannot change the tantrum, and stopping it doesn't resolve the emotions behind it - stopping it would just hit the pause button, and save it up for later. Best to get it out as an expressive form. Also, teaching/learning cannot happen in the heat of the tantrum. Then she needs love and acceptance. The gentle teaching needs to happen a few hours after the tantrum is done and you are both feeling better and stronger...
I hope this makes sense.
