The reason she is staying awake so long and taking such a long time to go to sleep is because of anxiety in relation to what will happen if you aren't there.
She wants you to stay. She knows that when she goes to sleep you will go. So she stays awake as long as she possibly can. This will keep you with her as long as possible. Even when she does go to sleep she will be going to sleep anxious in the knowledge that you will leave and she doesn't want you to.
So the answer is to face the anxiety head on. Teach her that going to sleep alone is nothing to be anxious about.
Once she has learnt that going to sleep alone isn't something to be anxious about, she will have no reason to keep herself awake. Once she is used to you not being there in the room when she goes to sleep, she will have no reason to stay awake so when she goes to bed, she will go to sleep.
So the transition to teach her to go to sleep alone is what will be difficult. But once out the other side when she has accepted things and the anxieties faced, there will be nothing to be scared about or any reason to cause distress.
I would go for Rapid Return. Put her to bed, "Nan night sweetheart. Love you. Sleep time now. Stay in bed and stay quiet please". Kiss, leave without delay and close door (obviously and loudly, not quietly and discretely - she needs to know the door is shut and she is alone)
Then wait. If she cried but stays in bed then give it 5 minutes, return and repeat: Put her to bed, "Nan night sweetheart. Love you. Sleep time now. Stay in bed and stay quiet please". Kiss, leave without delay and close door (obviously and loudly, not quietly and discretely - she needs to know the door is shut and she is alone)
If she leaves the room/bed you have to be rapid - get to her straight away and repeat: Put her to bed, "Nan night sweetheart. Love you. Sleep time now. Stay in bed and stay quiet please". Kiss, leave without delay and close door (obviously and loudly, not quietly and discretely - she needs to know the door is shut and she is alone).
Just keep on repeating over and over every time until she 'gets it' and accepts she has to stay in her bed and stay quiet on her own.
Once she has learnt and accepted that going to sleep alone will be the way it always is, she will no longer be anxious about it.