So I have a different take on this.
I don’t think anyone is as acutely aware of what’s right for your baby as you are. From what you say about her needing to be kept upright to sleep, I think she does have digestive discomfort. Likely cause is an allergy, but that may not be it. I think you should ignore the professionals and take things into your own hands.
She’s 6mo and you’ve started weaning. She slept well after the first week. Eliminate dairy for two weeks entirely and see how her mood is. It may or may not impact her sleep, but you’ll know if something is different. Just do it. Two weeks without cow’s milk (but with a good quality substitute, or making up for it in other ways) won’t harm her. You may actually notice a result when you reintroduce it.
Secondly, I KNOW it doesn’t feel this way when you’re in it, but she’s not doing this TO you. It’s not personal. She doesn’t know what she’s doing. I guarantee she wants to sleep. She wants to be comfortable, at ease, not crying, happy. Something is stopping her. She doesn’t know what, she couldn’t tell you if she did, and nobody else knows either. It just sucks. This is sometimes how it is with babies and it’s AWFUL. But there’s no alternative. You just have to try this and that until you hit on what it is.
Once I accepted that this was the baby I had and that I needed to adjust my life to that, I did feel better. The fight went out of me, in the sense that I wasn’t counting the minutes and hours and days until my life went back to what it was. I accepted that wouldn’t happen for longer than I had anticipated. I gave in, and I think my baby felt it.
To this day I feel guilty about how much I hated my baby up to that point. It wasn’t his fault. But it wasn’t mine either and I was besides myself with exhaustion and despair and hormones and all the rest of it. It changed me, for sure. But I’m many years down the line now. It does end. Feels like an eon when you’re in it. With hindsight, it was a blip.
Good luck. Just know you’re not awful, you’re not a bad mother, you’re not doing anything wrong. You’re feeling your way through a highly charged and difficult situation wearing a blindfold, on your knees, with little support and very lonely. It will end though. Promise.