Welcome to my world, this has been my DS since he was about three and he's now 8! He has had various times when we've thought we've cracked it (with him going to bed fine and happy with DH or I just visiting now and again to allay his anxiety about being alone) and other times when it's all an absolute impossibility for him.
We're currently in a difficult phase and I am drained. Dh and I take a night each to sit with DS while he drops off, which as he's anxious and worried at night, tends to be about 10om 
and he wakes every night and comes into our bed.
It's a modus operandi of sorts but it's not good.
We have just started working through a book called "what to do when you worry too much" and it seems good. Basically it's about accdepting that your child is anxious and a worrier, and putting in strategies to deal with it. Largely this involves getting the child to accept that the more you talk about worries, the more your parents reassure you, the more water you are pouring onto your worries and the more you are growing them.
IT's a bit counter intuitive for us all as DS has been used to feeling free to talk about his worries and as parents it's natural for us to want to listen and talk to him to try to ease them.
The book advises a 'worry time' for 15 mins each day, (not at bedtime!) and the child has to save their worries until then.
We found last night that worry time was worth doing, as we could identify that actually DS only had a couple of worries. As opposed to about a hundred good things in his life/things to look forward to.
I think it is starting to help. So perhaps try a book like this? If as you say your DD is an emotional person always, it might be worth having some strategies up your sleeve.
The thing with sleepovers made me smile because my DS is exactly the same. I think it's because sleep is usually the last thing on the agenda at a sleepover; and you're with others...and you just talk and have fun until you collapse through exhaustion, which is quite a nicer way to go than to lay alone worrying!
Good luck.