Loo, Ok, some ideas then. Probably not all helpful, but hey, i imagine you'll take anything at the moment!
D is obviously a sensitive baby, and i would hazard that she is very easily overstimulated. She sounds alot like Roh was with getting to sleep, he was terrible for napping, and used to sleep pretty well at night, but it would take ages to get him off. Firstly, if this problem has gotten alot worse since you moved her out of your room, i'd move her back, and hell, at this point, if she's not settling at night and no one is getting any sleep, let her back in your bed. Honestly, not losing your mind now has got to be top priority!
Also, you keep saying "she's got what she wants" when you end up takign her in the bed. Careful not to transfer adult motivations onto her, she's a baby, and still very young, and although routines can be habit forming, and therefore hard to break later on down the line, she isn't capable of the kind of manipulative thinking or planning you are projecting on to her. Its not like she's thinking, "if i just stay awake a bit longer, they'll give up and let me sleep with them". She's just unhappy/uncomfortable and wants comforting and safety.
I'm not having a go at all, i get so angry with Freyja at times, because it feels like she's doing stuff on purpose! I'm only saying this, because i find it alot less stressful if i hold in my mind the fact that she's not intentionally keeping me awake!
I'm assuming that when she wakes up she's upset and crying, so you need to go to her, rather than she's just waking up and calm? If she stirs and isn't upset, don't go to her at all! Just leave her to settle back down.
You might find that always having the room pitch black will help. I can tell you from experience that cardboard and masking tape works brilliantly to black out a room!! I'd suggest that as D is so sensitive to stimulus, that the point at which she is eye rubbing and yawning might be too late for her to nap, as she might already be overstimulated. Keep an eye out for when she starts doing things like, avoiding eye contact, trying to look/turn her head away from toys, waving her arms and legs more actively, and getting more vocal. Those are earlier signs of over stimulation/tiredness. Maybe try timing how long it is from waking up to starting to rub her eyes etc. and then maybe try putting her down 5/10/15 mins before that time.
In general babies this age can only cope with being awake for around 1 hour 15-20 mins before they become over tired, although it varies baby to baby, and also at different times of day. What helps is to have a nap "ritual". So 15 mins before you feel she needs a sleep, take her to a dark room, play a piece of soothing music (classical piano is great), and make sure its always the same music, maybe sing the same song every time. You could incorporate a feed in with it if you like. Perhaps have some lavender or something in her room, so she associates a smell with sleep time too. All of that will give her time to wind down, with minimum stimulation before she gets put down to nap. Then, like i said to L+L, try putting her down, if she gets upset, try soothing her in the cot, if it doesn't work, pick her up and settle her and then put her back down. Another idea is to put her down, and then sit by the cot with your hands through the bars, either holding her hand or with a hand on her back/tummy. Try to avoid touching her head, as some babies find it very stimulating, and try to avoid rubbing, stroking, as again its more stimulation.
Freyja falls asleep to her mobile brilliantly, but with Roh i had to make sure that there was literally nothing even remotely interesting visable from his cot, because the tiniest bit of stimulus would send him loopy!
As for the breastfeeding, you've really gone above and beyond with it, and done so brilliantly! Have a think about possibly cutting out a few feeds a little sooner than you perhaps planned though maybe? On top of all the sleep strain the fussy feeds, plus your worry with D's weight (which i know however much people tell you its ok, it must be worrying the hell out of you
) it might just be one battle too much?
Sorry, its taken me like an hour to post this!!!