Me again, up for next feed.
Some other thoughts.
You must beg, steal and borrow to get some sleep in the day if you can. I know the frustration of lying down and just nodding off, when a baby wakes and you think 'I won't even bother'. With my first dc, I just accepted it and didn't want to hand my pfb to anyone else, with my twins, I recognise that this is a total essential survival tool. Do you have parents, IL's, a kind neighbour, friends, who can organise a rota to take your baby for a walk around the park for 2hr slots mid morn, and mid afternoon, whilst you catch up on your sleep? Once yoy have caught up a bit, it goes without saying that you will be in a better place to tackle the sleep issues. My dh took my twins out at the weekend so I could do something with our two older dcs (no sleep unfortunately) and the babies slept the whole time and I had a break. This way too, dh gets to help in a practical way (ie at the weekend when he isn't - hopefully - at work).
If your baby needs more milk than you can supply, really don't be worried about using more formula, or ALL formula if necessary. There is a lot of pressure to b/fee (and am sure someone will come along to flame me for this), but with a little perspective (my pfb is now 5 years), I can see that whilst I exclusively breast fed him for a year, he is no healthier/bigger/as bonded with me than friends' dcs who were formula fed. If it isn't filling him up, its not the end of the world to recognise this and put in another plan of action.
I would second routine, routine, routine. I feed my babies a lot in the day (I think that the more they get in daylight, the less they will need at night) and my babies are recognising even now what happens at certain parts of the day. As I have always done a bedtime routine with them (its never too late to start), after 2 months, they have this week realised that 5.30ish means going upstairs for bath/wash, 6ish means feeding, and 7ish means lights out and sleep and they have gone down every night.
Right, back to sleep for me, good luck x