oh dear i'm so sorry you and she are going through all that crying and sleeplessness. it is so exhausting and so upsetting.
it does sound like something is bothering her if she is crying and screaming for so very long; it does not sound like leaving her to cry has taught her to fall asleep on her own and i wonder if it has reinforced her separation anxiety?
i also have big problems getting my LO to sleep (my older one sleep trained in one and a half days at age 17 mos using pu/pd, it was a dream, he sleeps thru the night since then, not the 13 mon old, nothing helped) so i don't think i'm the best person to give advice, but i can tell you that my LO also had long night wakings but when i started putting him a in crib and shhing and patting him to sleep that he always falls back asleep (the problem is that this has created a new problem, which is everytime he wakes up he expects that). if he's really tired i can just shhh and not even pat. but if he is really screaming i have to keep putting him on his belly and patting his bum or his back or rubbing his back, until he gets sleepy.
other moms have told me that once they get to the sleepy stage, where they are no longer resisting you, but only half awake, that you can start a program of walk in/walk out.
if she is teething, i have heard that teething tablets help, but i have no personal experience with it.
also have you ruled out any medical problem like reflux?
i'm very tired so am not sure i read your post carefully but i do think that if your LO will develop better sleep patterns when she has her own bed and is routinely put there to sleep at the same time.
i hope other mums have some good advice so that you both can get some rest!