That's your answer then really OP I'm afraid.
He doesn't see this problem for what it is.
He doesn't want to change.
His lifestyle is simply not compatible with that of a non hoarder or a child, therefore he cannot live with you.
If you want to stay in a relationship with him then he needs to go home and live separately.
If you don't want to be in a relationship where you live separately, you need to end the relationship.
For your children's sake as he will not change, the hoard will only grow back if you do manage to periodically cull it, and they will have to live in an environment that is chaotic at best at dangerous at worst.
I do appreciate that due to your little one's age and the issues with sleep etc you're on your knees and probably too exhausted to face this.
If it was another issue with him I might say wait it out until you are less reliant on him for support with the sleep etc but the problem with his issue being hoarding is that every week that passes is another week the hoard potentially encroaches further on your space.
And if by some miracle he does clear his old place enough to rent it out, enough of the shit from that place will have moved to yours and the job of getting him out again will be even harder.
I really feel for you, you're in an incredibly tough spot. Hoarding is one of the most difficult addictive behaviours in a way as it's tempting for people without experience of it to think they can sensibly reason with a hoarder and make them see sense.
But it's like telling an alcoholic to just have two drinks and not more or telling a drug addict to only shoot up once a day and not more. Logic and reason don't work. He would need to go home, have some serious therapy and work on himself individually to address these behaviours.
But he won't I'm afraid 