I hear you LN. The no sleep is just a killer isn't it. I'm finding that occasionally I will feed my little miss from both sides but feel like she hasn't reached that really content stage, and so I give her a formula top up when I put her down 20 odd minutes later. I'm not sure if our "issue" though is that my milk supply is not as plentiful as it could be, or if its because we've always had significant attachment issues coupled with #3 being a very lazy feeding, or a combination. I have no doubt the "hit by a train" feeling I have is doing my milk supply no favours at all.

I hope you can work out the logistics. A night of uninterrupted rest would I'm sure do you the world of good, and maybe the little recharge would be beneficial to your milk supply rather than detrimental. Good luck.