First off- solidarity. We've just come our of this phase and it was hideous.
Secondly: Your DH needs to pull his weight. That is a statement, not a suggestion. Having your level of sleep deprivation on a sustained basis is potentially dangerous when looking after a small child which I presume you are doing the majority of! I'm not saying this to scare you, more for how to phrase it to him. Unless he is a surgeon or operates heavy machinery for his job, he needs sleep exactly as much as you do, if not less. As a friend in the same situation said to me: if my partner doesn't sleep, he might f* up a spreadsheet. If I don't sleep, I might accidentally leave the baby on a changing table. At best the baby has mummy crying on her all day which isnt great either!
I'm pleased to day that the sleep situ could very well get better by itself quite quickly. For us we had 2 weeks of what you're describing- roughly hourly wakeups, sometimes more or less but like 6-10 a night. Then suddenly she has gone back to her old pattern of sleeping longer blocks of about 3-4 hours. Which is totally doable! Happened overnight, as did the beginning of the regression.
During those two weeks the cot was suddenly lava, naps were a nightmare, and I certainly resorted to feeding to sleep more often than she needed to eat. BUT that's where a partner comes in handy! They can't smell the milk on your partner so they will often be able to get the baby to sleep by rocking or patting which is good as it means that they have a variety of sleep associations. During the regression I could only feed her to sleep but partner could rock her. Now we are through it, she lets me rock her or pat her to sleep too unless she is really hungry.
During those two weeks we slept shifts. One did 8pm until first feed after 2am and then we switched, with DH bringing her to me for feeds or giving her a bottle if I wanted to sleep through- breastfeeding is well established now so skipping the odd feed wont hurt if she can take a bottle from your partner. Shift sleeping on sofa bed is annoying but honestly has saved us. Each person gets 5-6 hours sleep guaranteed, and it helps the baby learn to sleep with a variety of associations and carers.
I recognise that battling your partner is the last thing you need right now so if you can't do this right now, know that it's fine to feed to sleep each time if you have to, the baby will learn to sleep better and without boob developmentally in any case sooner or later. Its just that for the sake of your sanity it would help to be sooner and DH could help with that.
On the regression- it wasn't anything we did, she just one day started sleeping longer again. And it was only 2 weeks so stay strong! Of course all babies are different and if it goes on ages you could sleep train or something (plus baby sleep isnt linear etc and soon teething or illness or development will break it again- which is why its good to have shift system or alternate wakeups to fall back on with your partner).
Good luck!