Kuraisa, perhaps you have already tried this (and I admit I haven't read through everyone else's posts!) but is it worth trying to re-settle him just before the 40-45min mark? I know this works for some people and eventually the baby gets into a new groove and sleeps longer.
From my personal experience, I think you are amazing for doing this without much support. Natalie was unsettled for the first 6 months or so. There were some days I really didn't like her at all (even though I loved her because she was my baby, IYKWIM). But I was fortunate in that I had family nearby who I could visit, who loved her even though she cried all the time, and they gave me respite.
I found an afternoon walk provided a great time to recharge and she did sleep in the pram for 40 mins.
I found Tressillian were a brilliant help to me, and while I understand it isn't the same for everyone, I found they were very reassuring IRT 'normal' infant behaviour. I only used the over the phone service but I still found it helpful.
You might find there's an ABA group in your area? They may be a supportive group for you to be a part of if you think that'd help. (It could be worth a go in any case?)
I don't know what else to say. I recognise your desperation and I just wish I could help you. Can your DH take a sick day or a leave day before a weekend so that you can have a day and night off to rest (between feeds) then he can have the weekend to recuperate before work again on Monday? Things may seem a fraction easier to cope with if you've had a bit of a catchup on some sleep.
Take care of you, mate.