It’s good that you’re trying all of these techniques to try to address the issue. It does seem though that they aren’t working if she’s still not settling at 5.5
It’s not just the case that she doesn’t need much sleep, it’s that she can’t settle without you being there.
In terms of mornings, my DS used to get up early but at that age he would put on a dvd in his bedroom and watch it until I got up (probably for an hour or so).
I do get that it’s distressing to try to leave her when she’s crying and getting herself into a state, but it seems she has become so dependent on someone being with her that it’s having a negative impact on her.
It might be worth getting her a special teddy to help her sleep - take her to ‘build a bear’ and get one with a heartbeat, let her choose what she would like, then tell her that if she wakes in the night she’s to cuddle her special bear like she does mummy and it will help her sleep. Set up a chart and give her a star for every night she settles herself, maybe a star for teddy too because he helped her sleep. Make it a positive thing rather than her feeling like she’s being rejected.
She will be used to the rewards thing presumably from being in school.
Your DH needs to be on board with this, explain you’re trying to meet him in the middle and this is something that may help you all. If he does need to get up in the night he must not get wound up or tease her, etc, simply say “is teddy not helping tonight” and if she says no, he takes the teddy away and sits with her. He doesn’t necessarily have to hug her, etc if he’s tense, just tuck her in and be there.
Explain it would be really good if he could step into this rather than you having to go in, because she is so dependent on you. When she gets used to teddy being taken away she may start to settle with it because she wants to keep it with her.
If none of your attempts work, you really should consider taking her to the doctors and trying to find out what’s going on.
The fact your DH has given you a timeframe to decide if you want a divorce means that he doesn’t and he just said it in haste because he was hurt. Take some time to think about what you want. Discuss your boundaries and give him chance to step up with your DD in the next couple of weeks. Only you know what is right for you