Jill, just wanted to answer your specific queries about the chair/floor and add some other stuff I've learned in the past 6 months or so.
Ds2 spent loads of time in his car seat or in the chair. If they slump it isn't so good because their stomachs get squashed. We borrowed a Jane seat from a neighbour, where you can adjust the angle, and this just got moved from room to room. For a few months this was the only place Ds2 would sleep.
But I found that at certain times of day it was okay to put him on the floor. Not immediately after a feed, obviously, and it does take a bit of trial and error, but if it was long enough after a feed he could lie happily for a little while on the floor and so I didn't feel I was stunting his development so much.
A couple more things that helped:
Massage. It helps to move things along the digestive tract. I built it into our evening routine, with him lying on our bed, propped up with a pillow under his head and with lots of towels around . If dp was around, he looked after ds1 during massage time, if I was on my own, ds1 came in to 'help' with the massage (we sing songs together while I do the massage and I try to stop ds1 from bouncing on the bed too much );
A baby carrier. One that holds them upright but doesn't squash their stomach too much. We have a Baby Bjorn but I'm looking for a better one because it hurts my back if I use it too much. But Ds2 does like being in it. It helps the milk to drain from his stomach. It allows me to do some stuff around the house or with ds1 and ds2 doesn't feel like I'm ignoring him. It's also good for short trips to the shops/library/playground etc. - the buggy hasn't been used much as he sits in a funny position and seems pretty uncomfortable.
Ds2's reflux did seem to get better once he could sit unaided. I can't remember at what age this was though!
A word of warning about solids:
Many doctors/HVs/other mums will recommend starting solids early (i.e. before 6 months) with a refluxing baby. They certainly did with me. But research has been done that shows while solids may appear to make reflux better (there's less vomiting) they can actually irritate the oesophagus more and there's also risk of aspiration (solids going into the air passages). Plus some cases of reflux are due to food intolerances and so starting solids before 6m might make these worse. Unfortunately the medics don't seem very up-to-date on this research.
That reminds me. You don't say if your dd is on formula, breastmilk or a mixture. Changing formula might help. Or if she's breastfed, trying to identify if there's something in your diet that she's sensitive to. There's probably some info about food sensitivities on the sites I referenced before.
Cranial osteopathy didn't work in our case, although some people say it really helps.
I guess every baby is different, so you can take whatever's helpful from my masses of information here! I wish the cranial osteopathy had worked, though. I completely agree with everything you say about how stressful and demoralising feeding can be. My emotions go up and down like a yo-yo depending on how well a feed has gone. And it may sound cliched, but I really think that people can't understand how difficult it is unless they have looked after a refluxing baby themselves. I saw my midwife again about 3 months ago and she told me that he would grow out of it. Well, that's not very helpful I'm afraid . Luckily the same day I met another mum with a 4 yo who had had reflux as a baby - so not only did this mum really sympathise, I could hear the details of how her dd had been treated and finally came off the medications with no more reflux. Which is a lot more helpful than just being told that they grow out of it eventually.
Best of luck with your refluxer.