feedtheyak, what a good idea!
Dilemma you are chronically sleep deprived, you poor thing.
If I were you I would certainly do this and get a good night's kip. If not too broke, why not make it a weekend in a nice hotel with pool etc?
Have you tried a star chart with your DD re the nights? I wish I'd tried one earlier with my ds, he really responded to it. He needs to earn a star each night in order to earn his pocket money on Saturday. We make the pocket money generous so that he is truly incentivised - he knows he can buy a star wars figure or something
Perhaps you could start with an immediate reward - tell her if she stays in her own bed all night, the sleep fairies (or whatever, dunno if she's a fairy kind of girl) will pay a visit and leave a special present for her.
At the moment the message to her is not clear enough - sometimes she's put back, sometimes she can stay with you - but it sounds always more or less accepted that she does this. Think you need to tell her clearly in both words and actions that you don't want this to happen any more.