Op here. Thanks all, will see what children's centre has.
Penguins is right, it's about daytime sleep. For whatever reason (circadian rhythms? The dark? Pixies??!) I can move her at night - between 10 and 4 I'm usually ok to get her in the crib, so long as I wait 20 mins, and then she'll sleep for a couple of hours, which I totally accept, although of course would prefer more ;) - but her daytime sleep is so shallow I literally cannot even reposition her now, let alone get her in a sling, pass to someone else - which i used to be able to do - or put her down. I'm holding her sitting down for hours a day, including all evening up to at least 10.
I breastfeed, pottering, which is what got me here in the first place, because I foolishly bf her to sleep and now she won't take any other way without a massive screaming fit. If someone else walks her, yes, she'll eventually pass out after crying, but then they have to sit with her instead (if they're lucky enough to occasionally manage to sit down without waking her)!
Strollers and the car are in reality a sort of cry it out, because she'll be happy in them until they make her tired, then she'll cry due to lack of boob to get her to sleep, until she exhausts herself. And then as soon as you stop moving... She wakes! I have tried bf to sleep lying down, but she wakes within 20 mins even if I don't move her, which is why pu/pd just was so horrid for us; if you get over the pain barrier and she falls asleep, you're back where you started 20 mins later when she wakes up realising she's not being held!
I dread the day the night magic doesn't work and I only get 20 mins instead of a couple of hours relief, so I'm desperate to do something!!
Thanks for all suggestions; all gratefully received!