Hi I posted with almost exactly the same issue! First of all it's totally, totally normal and things do change. Really they do. We co-slept (dd on my side of the bed, me in middle) while she was tiny. I was worried that it was going to cause problems with sleep associations, particularly as some nights she slept on my chest as well.
She also hated the Moses basket with a passion. In the end, when we were both not getting too much sleep, we had a look at how she liked to sleep and re-created it in her basket. So, we slightly tilted the mattress and rolled up a towel so it was kind of like having an arm behind her. I also put a pajama top over the side for her to snuggle in to or wrapped her up in it before putting her in
It is tough and we had weeks where we would gently place her down once she'd nodded off, only to wake up seconds later and we'd have to do the whole rocking/feeding thing again
This may get me shouted at but my dd had no idea how to fall asleep by herself and stay settled so one night out of sheer physical and mental exhaustion I left her to cry for a few mins. She learned within a few minutes how to fall asleep.
All these things are just ideas for you to try plus I would say a pitch black, quiet room helps too along with a consistent nighttime routine BUT above all please be reassured that it does get better. That's what I was told and while I struggled to believe it, it really does. Now at four months mine is just beginning to think about waking up once and sometimes goes through. You'll get there and you'll make good decisions for your family.