Sorry it took so long for me to come back...
Thanks everyone for all your ideas and advice. I've tried out almost all of them and with a bit of trial and error, I've found a method that eventually puts DD to sleep. About 1.5 hours after she wakes up, I look out for her sleepy signs. If I see any, I take her to our room, close the curtains, say night-night to the world outside (lol), put her in her sleeping bag and then walk around while singing "In the jungle, the quiet jungle, the lion sleeps tonight...". She eventually falls asleep with some grizzling but without the full blown scream/wailing for hours that she was doing. As long as my back holds out, I'm happy to have a method that puts her to sleep.
If I try to shh instead of singing, she screams. So I finally have an audience for my out of tune singing! So I came upon that by trial and error, cos I don't tend to sing a lot, being totally tone deaf!
I also have the radio on during the day, and will work on putting her down drowsy instead of fully asleep. But first, I'm going to work on extending her naps. I always run around during her naps, and am never in the room when she is about to wake so that I can pat her back to sleep. But I will try.
This isn't exactly self-settling, or even low effort, but I don't mind (at the moment). I'm just glad that she isn't screaming herself hoarse. ALthouhg, it's really only been one day and I don't want to jinx myself. Oh, and the last couple of nights she's been waking up every hour or 2 which is just exhausting, but I'm hoping that once the naps are sorted, this will sort itself out. If not... I'll be back with another thread!
Thank you everyone for making me feel liek there's light at the end of the tunnel.
PS I don't know who said this, but I read No Cry Sleep Solution, Baby WHisperer, Baby Love, Sleeping Like a Baby, The 90 Minute Baby Sleep Program... I think that is all! And I found the No Cry Sleep Solution had lots of ideas that didn't seem cruel and the 90 minute sleep program gave me permission to stop trying to settle DD after 15 mins and try again after 90 mins!
PPS KatieRabbit Its good to know that someone out there does feed-sleep-play. That makes so much more sense to me. I'm sort of feeding her every 3 or 4 hours, whenever it seems to fit in around her sleeps.