Op I could have written your opening post word for word apart from sleep trainer, our hv told us quite bluntly that she couldn't help.
We kept a sleep diary, I was up to him 16 times in one night....this was my night...EVERY NIGHT.
I was so tired constantly, I felt dizzy, physically sick, couldn't concentrate, most of the time had double vision, I was bone drenched utterly utterly exhausted.
Traumatic birth, pnd, and zero sleep has poisoned my relationship with him..my child.
He slept his first block of 6 hours when he started school, aged 5. I thought he was dead, I ran into his room thinking he had died!
Over time we got a few more nights of him sleeping longer thank God.
I accepted (rightly or wrongly) that this was just the way it was. I took each night as it came, handed over to dh the moment he walked in the door, went to bed (when he wasn't screaming and creating because he wanted just me) .
He was/is a very very challenging child. Behaviour was difficult, I couldn't leave him in a room on his own, he was destructive, overly active, a climber, a bolter, an escape artist. Dismantled my stair gates, regularly got out of car seats/high chairs/pram straps. Needed 100% attention constantly.
He now sleeps, he is a teenager.
Of course there was NO way on God's green earth we could consider another child and put ourselves through that again, hence the huge gap between my kids.
They are like night & dat thank fuck, child number 2 is so much easier.