I second that. If he's not fitting into all of the sleep training stuff, let it go. Naps seem really important - my daughter is mental if she doesn't get enough sleep during the day!
Are you breastfeeding or bottle feeding? Either way, is there anyone who can help with the nighttime feeds? If you're BF you could pump in the early evening so you could get a few hours sleep. If you're bottle feeding could you take the night off?
Unfortunately for new parents, babies are designed to wake through the night, it's a natural rhythm as well as a protective factor against SIDS so they dont fall into a sleep that is hard for them to rouse themselves from. Don't listen to anyone who suggests he should be sleeping through at 10 weeks - that's bullshit! The NHS don't even recommend routines till they're post 12 weeks as apparently they're too young to recognise them.
I'm sorry you're having such a hard time, the sleep thing is a fucker, really hard going. My DH has MS and I've seen how fatigued he can become with a new baby and i'm EBF so he gets much more sleep. Is there anyone helping you? If not, can you rope in a friend/mum/family member for some relief
Stick with it OP, get as much help as you can and let your little boy sleep as needs it. He will find his own groove and you'll find yours. You sound like you're doing really well, despite it being so awful.