Op, you were really clear in your post you are at a loss. No one needs to jump on you for being in that place.
Ideas, strategies, parenting tips, neat things that someone else has discovered... We've all needed them and used them at some point or another.
None of us are a complete knowledge bank of an alternative approach to the one we're trying that isn't having the desired effect.
At no point op have you given any impression that you are settling for this, accepting this, tolerating this, oblivious to effects on others, not bothered to impress on your DD the importance of this, taken the oath of least resistance etc... You have done none of that...
But yet, you need fresh input. It's especially important when there is only one of you in the house who is an adult (lodgers irrelevant obvs) because often it's in the discussion of ongoing things that an 'ah-ha' moment happens, a 'why don't we give this a go...' type thing which only happens in a two-way dialogue.
When life is coming at you like a relentless conveyor belt and you don't have a sounding board, it's really hard to change tack and come back with something fresh to try.
Well done for seeking support op, and I'm sorry that you've had such a lot of criticism which could certainly have been offered more constructively. You asked because you cared and want to find a solution.
Of course we haven't seen this dynamic at play which would help for suggestions, but personally, I'd be looking to have a conversation not in the heat of the moment where you set the basic 'homework isn't optional and we can both agree on that' baseline and then move on to questions like, would you rather get up earlier and do it before school? Does it help if I do some work at the same time so there is a school-like working atmosphere... Etc
Adding in, the screaming must stop, if that happens again this (xyz) will be the punishment (something that she cares about but isn't her emotional security, so her gadgets but not her security blanket).
My DD is a bit like this, she hates doing homework when she's interrupted and told to do it cos she can't switch her focus quickly from one task to another.
She will do it happily if the day before, or earlier in the day, I say things like 'we'll get home from school, have a snack and then do ten minutes of homework, after that we'll walk the dog and you can chill out while I cook tea...'
She likes to have a mental map of her day, even when she 'knows' homework needs doing she hates it being mentioned on the spur of the moment.
Which is frustrating from another person's perspective cos it's necessity is inevitable so entirely expected... But to her she feels it is sprung on her (and she's too young to take her own responsibility for it yet, so it's on me to make sure it happens).
I'm similar though, and when I was a kid I liked to get up early and do it before school, so I could get home from school and switch off.