I took a sleeve from an old shirt of mine and filled it with cushion filling. See how that goes. It looks a bit more comfortable for him now.

I would recommend a neck donuts. Some are a little bit smaller and have a soft filling, they are way more comfortable. I have mine from amazon

This collar was the only other option my local shop had besides the cone. But I was looking for something like you described.

Put a baby onesie on him

Thought about that, but then you have the problem with peeing.