I think the manipulation line is a bit of a stretch, but I can kind of see some logic to trying to move her further away to see how it goes. I mean if you try it and it helps - win, and if it doesn't work just stop and go back to what you were doing before, no harm done.

When DD1 was a couple months older than your DD and waking up LOTS at night my GP suggested trying moving her out because as they get older they get more aware of what's going on around them and are more likely to get woken up by you moving around, going to bed, rolling over, snoring etc. Then even if they aren't really hungry they are awake and just think while I'm up I might as well have some milk, or if their sleep cue if BFing then they may just be looking to BF for sleep not for the milk.

Anyway we moved DD1 and I would say it halved the wake ups. She did still wake up for milk and also from discomfort related to getting her first tooth, but there were less 'incidental' wake ups that lead to a BF even if that was not really why she woke in the first place ITMS. But as I said, give it a burl, if it doesn't help just stop.
^ This
We had almost the same situation. DD2 was in her bassinet on my side of the bed until around 8.5 months. She slept so well until about 5.5 months when the hellish nights started I was up to her SO much over night and, like you, was only getting a few hours broken sleep at night on a regular basis. Wonder Weeks and cutting teeth certainly didn't help!

Anyway, I tried everything I could think of with no real success. I just couldn't work it out, especially as she had slept so well on our holiday at 7 months. So I spoke to my CHN at DD2's 8 month checkup (she was a great CHN for a change!) and she suggested trying her in her own room as a last resort. She didn't agree with CC or CIO and said it may be an inconvenience for me for a week or so but she thought it could definitely help. She thought DD2 and I were probably a little too in-tune with each other and waking each other (prempting feeds, hearing each others noises, etc). Well I think she was right cause DD2's sleep improved dramatically and, of course, so did mine I have got a sound and movement monitor though so that made the transition easier for me too.

I know my DD is older than Miss A but I had to share. Maybe just moving her elsewhere in your room might help. DD1 slept in our WIR, our ensuite and just outside our bedroom door before I moved her to her own room. She happily went to her own room around 10 weeks though and was a freak when it came to sleeping. I sometimes wonder if moving DD2 to her own room earlier would have helped at all

Good luck with your decision and getting more sleep. I don't recall DD1 having night sleep issues like DD2 did but from what I read online, it's quite common from the 4-5 month stage. The big WW at 19-20 weeks is often the starting point.