F the other shit that needs to be done in the house. It’s either that or slowly growing urges for infanticide. Your sanity is more important than keeping up.
The only way my youngest could sleep is when he was on me (specifically on my left shoulder in the glider chair after walking about a mile holding him there. The right shoulder was not good enough for him. My left bicep would burn like a sonofabitch). And I learned to sleep in that uncomfortable dammed chair. He was happy, so goddamit, I was going to be happy enough at 3AM.
Besides, the top part felt great, he was very snuggly. It mitigated the lack of lumbar support, butt-cushioning, and shoulder ligament tearing that was happening on the back.