sheen, no wonder you are knackered, but it sounds like you are doing all the right things in feeding on demand . I don't know if anyone's told you that babies feed at night as this is better for stimulating your supply (and I suppose it's a throwback to caveman culture when most predators would be out of the way, so safer) so your baby is doing all the right things as well.
I agree on the getting some sleep whenever the baby does as well, and if possible, can you try and sneak an extra couple of feeds in during the day in the hope that this will help your DD go a bit longer at night (it might not work though). And enlisting the help of DH would be good. Normally it's easier to express first thing in the morning, so if you could get enough then, or by topping it up through the day, for a 5 or 6 oz feed, then DH could do one of the night feeds for you, say the 11 o'clock one, and allowing you to get a decent chunk of sleep before having to get up again. And, if introducing a bottle of formula is what you want to do, by four months your supply should be well enough established that it shouldn't interfere too much. Some women give a bottle before bed, then express what the baby would've had and that can be used by hubby to feed later in the night.
If it's any comfort, 16 weeks tends to be a bit of a turning point when supply/demand gets really settled and the baby starts to fall into their own routine so fingers crossed you should be getting a bit more sleep soon.
sausage....I'm sure you made some very good points in your post, but it is very difficult to read as a single paragraph of only three sentences! I'm afraid I glazed over after the first few lines