Hi, new mum and dad, I had a new born boy with the same problem as depicted. He cannot be swaddled, when approaching 4 am or so, he just keep squirming, which no amount of cajoling would work for him to settle down. We are not experienced parents, we would like to share how we cope with this situation. As losing weight may be the direct consequence, whilst my wife may love to.
I normally hold his little hands, refraining him squirming in terms of well fed and patted. He may not feel happy but you need to stand firm to guide him. At this very moment, we need to apply the silicone soother to settle him down. At the mean time, I laid over with him, letting him awared you being with him, increase his sense of safety. Till the day break, he successfully has been settled. Namely, at 4 to 6am, either one of your pair should accompany the new born. I trust your new born girl could be settled in the same way.