OP, let me first say that I think you would benefit the greatest by finding a trainer to work with and take lessons from. I think most of your problems most likely stem from lack of correct timing.
If a cue is released too soon or too late, the horse doesn't correlate the correct answer to the request.
So, basically, down to my question. How do I get her listening to me in an open paddock? How do I make her stop running away on me with her head in the air?
and how do I get her to curve into the turns I'm asking of her rather than pushing her whole body across?
Personally, I would take this horse all the way back to square one. Act like she's never been handled. Start from scratch like you would a colt. It sounds like she has some serious holes in her training that have never been properly fixed. She doesn't understand your cues and/or she doesn't want to listen.
bolts or throws her head up as soon as you take the pressure off the reins
This suggests to me that she hasn't been taught to actually properly give to the bit. And suggests to me that you often release your cues too late
when she tries to give you a correct response - she gets frustrated, and doesn't know what you want, so just ignores you completely and takes advantage of when you "let her loose".
Sure, it does take a horse lots of time and training to learn to "self-carry" their head in an acceptable place, but if she's immediately throwing her head once you "let go" of her, then I would say she's never really learned how to be soft to the bit and only wants to fight it and/or evade it.
I lunge her for 20 minutes before I ride, and that definitely seems to help.
What exactly do you mean when you say lunging? (I only ask because it means different things to different people.) Please be more specific.
When she scoots/bolts/jumps/does anything stupid, I'll stop her, back her up, make her wait for a few seconds and then continue on again.
If you think about this, what exactly are you teaching her?
You are teaching your horse to stop and back up ..... when you didn't necessarily want her to......
If you want to teach her to listen to you, then you have to teach her to listen to you. Instead of stopping and backing her, you should continue to try to get her to do what you were originally doing.
My trouble is though, when I'm trying to trot and canter (particularly canter) in a large paddock as opposed to a small arena/round yard, she'll run for all she's worth. She's extremely head strong,
Again, if she's got holes in her training, they are going to be much more obvious when you get out of a smaller area.
and turning her in circles causes her to scoot inwards on a diagonal, rather than actually curving into the turn if that makes sense? I'm doing all the right things, and using my inside leg to push her body out while I turn her in, which works when she's engaged and listening, but is falling on deaf ears when she's in this psycho mindset.
You need to figure out a way to MAKE her listen. The more you "nag" the more it falls on deaf ears. So make your cues mean something. Ask nicely once, then ENFORCE if it doesn't happen.
But again, you have to have the appropriate timing. If you are releasing your cue too early or too late, she's not going to make the connection.
I do still think you need to go back to square one with this horse and teach her how to correctly respond to a cue, but I do think you would benefit greatly by finding a trainer to help you. Because they can watch you in person and give you feedback on your timing and/or show you in person. Very hard to do that over the internet.