Hi there! Welcome to the BW community
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With regards to the EW's, I think you need to choose a time you're willing to accept as wake up time and what qualifies as an EW. For me, generally my boys sleep until 6:30/7am. I hate waking up early but really, they've been asleep for 12hrs, they're all topped up on sleep. I would treat the 5am wake up as an EW and if she's hungry, give her a bottle. You could make it a smaller one than usual if you're worried about it affecting her 7am bottle.
I followed the routines in the book mostly for DS1, for DS2 I modified it a bit to suit our family. I did cluster feeds at 4 and 6 until DS2 was on three solids meals a day and I keep my boys on a 7-7 schedule (the wake up is negotiable, bed time is not)
Try not to focus on rigidly following the specific routine in the book. The whole premise of BW is that you learn to read your child. My DS2 can usually stay awake for 3hrs but there are some days when he's rubbing his eyes at 2.5hr and so I lay him down for his nap early. I generally find when I do that, the nap is not negatively affect. If anything, he naps a little longer because he's not waking from OT.
I don't consider helping your baby relax 'giving in'. Your baby looks to you for comfort and if she needs a little help winding down, so be it. Maybe you could just incorporate that into your wind down routine? For us, wind down is pretty quick. Into the sleep sack, one story (if that), a little cuddle and then into bed. DS1 liked to take a little longer so just consider whether your baby needs a little more time to relax, or perhaps you're taking too long. It can take a bit of figuring out.
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