I used to work with behaviourally challenged students whose behaviour impacted on everyone in the class. One of the best pieces of advice I had was the '3 class rules - and consequences if broken'. I mean 'big' rules (no hitting others, that kind of thing) along with (for more minor behaviour issues) a yellow card for a 'first offence' (so a clear visible warning) and then a red card and a suitable consequence if it happened again. And the consequences had to fit the misdemeanour and at the time, not be something random implemented the next day.
I know it's not as easy at home to implement all of those things in the home, but I did use them all to some degree, with adaptations, with my DSs. So maybe, Polly, you and the girls sit down and agree the '3 big rules' that have to happen at bedtime - e.g. 'We must get into bed and stay there when mum says' for one, maybe 'If we can't agree on a story choice, mum will choose for us' etc. With consequences linked to the rules (if not already 'built in' to the rule, like the mum choosing the story if they can't agree). You might also want to back it up a bit by asking them which rule they haven't followed - this helps them link it all together - behaviour rules are there for a reason, and not following them has consequences for them.
It's going to be a bit harder because you know Geller won't do it, but if it's done at your house, and you're really strict on it all for the first couple of weeks, you'll probably find their behaviour at bedtime just becomes better all-round as a positive consequence of the work you've all put into it.
A bit worried I'm sounding a bit 'preachy' 
but I promise you, it's worth a try. The child I was failing to manage at school before I had the help with the behaviour management went from being a hugely disruptive influence in September, to being a lot more calm, and able to sit and do his work without causing flashpoints, by half way through the school year. (Which made the rest of it so much more pleasant for everyone!) I was exhausted mentally, and I didn't always have the support of other teachers when he was elsewhere in the school, but if his mum sees me around, she still thanks me for how much she benefited from the school routines being used at home too. (Tbh, the boy, who was 7 at the time, likely had ADHD, but 30 years ago no one had heard of that, we only had one TA in the entire school shared between 7 classes, the Headteacher had no advice, so it was down to me!)
The girls are old enough to understand why you need bedtime to go smoothly, and you'll get there in the end Polly. We're all in awe of how far you've come and what you've achieved already! You'll achieve this too!
Gosh, that's a bit long, sorry.