You poor thing! I'm shattered all day when I'm up to feed twice in the night! I haven't been through this, but I have done a lot of reading, and it sounds like she's snacking, ie, having very small meals and therefore needing to eat frequently, and that she and you might benefit from larger meals, less often?

You say that you're 'already shoving a boob in her mouth far more often than she wants it'. When she cries during the day, do you presume it's from hunger and use the boob as your first option to help her? She will probably take it for comfort, regardless of what the need was - and it works - but if her need was for something else (wanting a change of scenery/activity, tiredness, uncomfortable due to wind, heat, cold, etc) then using the boob will just promote snacking. You might need to find other ways of comforting her or meeting her needs when she cries from something other than hunger, like changing her nappy, changing her position (put her down to play on the floor if you've been holding/babywearing, or pick her up if she's been down,) talking, singing, stroking, dancing, or even putting her to bed if she's tired. That will help her to go longer between meals, therefore eat more next time, therefore be happier to go longer before the next meal, etc. Hopefully doing that during the day will help also at night.

Re giving her a bottle (of your expressed milk), I've read that some babies won't take a bottle from their breastfeeding mum, but will from someone else - ie, why suck from the weird bottle when they know there's a lovely nipple right there??

Does she start the night in the cot? It might be worth getting DH to try to settle her, while you keep your distance, until a reasonable amount of time has passed since she last fed. Again, when she wakes, her need may not be hunger, it might be that she just needs reassurance/comfort/help going back to sleep. She's more likely to accept that help from her dad to start with, because she's so used to help from her mum coming in the form of a boob.

Again - I haven't been through this, but I hope that some of the ideas help - I think it's worth trying all sorts of strategies like these rather than just accept going on with that level of horriblle sleep deprivation.