Hi again OP 
Did you Google 'fourth trimester' like I suggested on one of your previous threads?
Both of mine are/were non-sleeping Velcro babies who just want to sleep on or with me. It's a horrible shock to discover that babies don't just automatically have an association between 'cot' and 'sleep' isn't it? 
I know you didn't want to consider co-sleeping, which I also didn't want to do with my first, and you said The Lullaby Trust advise against it. Their main advice is in a cot/Moses basket, but they also explicitly state, 'We do not tell parents never to bedshare.' They also have this leaflet which gives some advice on safe bed sharing. You'll also find plenty of threads on MN on different strategies people use to co-sleep safely. I did it from the start with my second, after having co-sleep for the better part of a year after several months of trying to battle DS1 into a cot, and I honestly think it made him happier to go into his own space because he got that earlier attachment from me.
BUT getting him to make friends with his cot took a while, and I started with full co-sleeping, then co-sleeping for the latter part of the night when he really didn't want to go in the cot again, and eventually he was happy to go back into his cot after every feed. He's still awake every one or two hours, but he's at least back in his cot and I can sleep in between with pillows and a duvet.
I used a hodge-podge of strategies from The No Cry Sleep Solution, Happiest Baby On the Block and pick-up, put down to get him in his cot and falling asleep there. Swaddling was the main thing. Yours may be getting a little old to introduce it now, so loose wrapping in a blanket that's she's in while you feed her may suffice. A gro-bag may be OK as suggested by a PP but ideally it should cover her arms so she gets a womb-like feeling. Maybe even try loose swaddling then stick her straight on the boob to calm down her initial hatred of it. The advantage of it is it makes her feel like she's still being held, even when she isn't. You Tube has lots of videos on different swaddling methods. DS2 is still swaddled all night long and for any cot naps at 21 weeks. Other naps are either on me or in the sling.
The second thing which was, and still is essential, is white noise. I've got a white noise app which runs all night and for all naps.
When you put her down initially, put her down in side-lying - either supporting her with your hand, or rolling something up behind her back like a blanket or a muslin. If she stays asleep, supervise her for 15-20 minutes then very gently ease her onto her back. It took weeks of putting DS2 down like this, then picking up at the slightest squeak, then putting down again, then up, down, up...etc and now he's fine just going straight in on his back.
I know you've not had success with a dummy and, again, she may be getting a little old to successfully introduce one now.
It does sound like she may have something like a silent reflux complicating things. Additionally, I would strongly advise trying an elimination diet. The main culprit is dairy, especially with refluxy babies, but soy is just as common, and frequently they have both. If you can stand it, completely eliminate dairy and soy from your diet for four weeks, then re-introduce one at a time. Soy is actually the hardest to eliminate - they sneak it into everything (all bread, for example - check labels). WRT dairy, Green and Black's dark chocolate with mint is dairy-free, hemp milk is best in coffee and Oreos are vegan (Can you tell I found an elimination diet while breastfeeding and not sleeping utter hell?)
Sorry to hear you're still struggling, but honestly that great mantra is so true: This Too Shall Pass. Possibly not for many months (I still have to turf my two year old out of my bed...) but one day it really will feel like eons ago, even though it feels never-ending now. 