Thanks for the supportive comments!
Having thought about it and chatted it through with DH, I think we are slipping into bad habits to "get through" each day, which is easier in the short term, but means we slowly move backwards. So, although it is going to be tough, we've decided we need to change things with a longer term aim in mind.
As of today we are going to alternate putting her down to sleep so that the stress of it isn't only on me and to try to break the sleep association with me. We are also going to try a slow no tears self settling technique. It will take longer, but for us I think it will work better than cry it out.
No idea what to do about the early morning wakings. I'm convinced she's still tired as she wakes crying and is grumpy until she has her first nap, but I just can't get her to settle, even cuddled up on me. I'm hoping that if we manage to get her to self settle, the early morning issue will somehow miraculously solve itself!!!
In good news, I started making puréed veg for the freezer in anticipation of weaning her in two weeks. Baby corn really does not purée, so I'll have to save that for when she's a little more used to food and ready for texture. But she was watching me make the purées like it was the most fascinating and hypnotic thing ever, so I gave her a tiny taste of carrot, and she was quite excited by it! I think she'll love it when we start properly 