Could you perhaps find a shared system? DH and I both work full-time, but his shift patterns and working hours mean that he is often at home when I am at work.
He will quite often blitz the washing and I will come home and he has done 3/4 loads. We have the grandchildren a lot, so have our own washing, all their clothes, bedding, towels etc.so there is a lot of washing these days. He typically washes, puts everything on the line, airs on the radiator and I come home to a huge pile of clean washing, which I fold, iron, put away as appropriate.
He doesn’t do it the way I do, I would prefer to do one load, dry it, iron it, put it away, but that doesn’t mean I am right, we just have different ways of doing things and when I come home and the house looks like a Chinese laundry I have just learned to be mellow about it.
Could you find a way of splitting the process so that he still feels like he is helping but you can work together to reduce the damp clothes being put away etc. I do hope you get it sorted, it would drive me potty! Good luck