Sweetheart,
Remember I told you how Charlie woke up every two hours until he was a year old? I know it made me a cranky, moody zombie and I hated it but my best advice to you is very similar to MadB's: do whatever is easiest.
I just went with it. I put him in bed with me and I did what I needed to for him to settle as quickly and painlessly as possible. And eventually he learned to self-settle. And that's the thing: self-settling is something they eventually learn - some sooner, others later. Though in Miss I's defence, the poor thing has a uncomfy brace on and I don't know if I could self-settle if I had to wear one of those all night.
So while you're going to have to do this anyway, take the path of least resistance. Feed her and doze while you do. And if you are becoming a zombie, ask a friendly neighbourhood husband, relative or friend ( ;) ) to babysit for 3-4 hours so you can crash for a little bit. She's doing BLS so honestly she won't starve in that time.
So my advice is more about finding ways for YOU to get more rest than finding alternative ways to settle her, because as you know, trying to put in new 'methods' in the middle of the night is not conducive to sanity.