OP, I can't say there is anything I can pass on to help, sadly, as I'm in the same dilemma, only mine is easier than yours because it's only with two children and not three, but yet I still manage to feeling like I'm drowning every single day. I thought it was either a sign of how much my children misbehave, or the fact I've got ms and my disability is such a challenge that I can't cope as well as everyone else, but I suspect it's actually that bedtime problems are a real thing for most people.
I have the problem of both my 7 and just-turned-4 year old wanting me to be with them while they sleep. The 7 year old 'humps' for comfort if I don't, and made himself sore doing so. So it's really important to me that habit breaks, and he learns to sleep without grinding himself on hard objects.
So I bath them together. It's loud, messy, and often fraught with fights, then 7 year old gets himself dressed while I help dress 4 year old for bed. They're both well capable of dressing themselves but if I don't, it doesn't get done because they'd rather play.
At the moment I play a shared podcast with them both, as my MS doesn't allow me to read two stories, and I struggle to even read one story at the moment. We alternate in whose room the podcast is shared, and who chooses the podcast. Then I settle the little one first, while the 7 year old reads quietly to himself in his room. It helps that he's a bookworm. Sometimes he will come and interrupt me settling the other one, and I have to protest that by doing so, the clock of waiting has just been put back, because he's 'woken' the youngest all over again.
Then, eventually, when the youngest is asleep I go in and do it all again with the eldest.
Recently I've taken to sitting between their bedrooms by myself, answering texts or emails, so they know I am there and yet they are learning to sleep alone. I'm hoping it still stops my eldest from 'humping' but it's early days so we shall see.
The 4 year old often comes out to check I am there, under the guise of needing a wee or another cuddle, but its always met with "straight back to bed after" and so far its working.
I have no idea how I'd cope with a 12 month old in the mix though. I hope someone else can come along and give you a helpful answer, maybe I can learn from it too!
The only thing I'm wondering is, does the 12 month old sleep with one of the others? If so, perhaps is try to treat them like one bed room settle, if you see what I mean? Other than that I have no idea what people do!