I think we have finally found a technique that works.
limit the input. Kids now have 5 'every day' out fits, 2 'good' outfits and a few pairs of PJ's. This allows for wet days when the washing won't dry without tempting me to stop laundry for a week!
work the handmaidens! I have two washing machines. Yes, it is thoroughly decident, but I know people with three TV's and my kids have been known to watch the washing machines instead! I refer to them, the dryer and my dishwasher as "the handmaidens". It is my job to make sure they don't slack. I have times in my routine when I 'feed' them plus catch up times on Monday or if we have disasters. My goal is 4 loads daily, more if needed, and on Mondays I do as many as I can, making use of the drier as needed. There is usually at least one of clothes, one of nappies then the rest I make up with more clothes, towels (I wash twice a week) and sheets (once a week). I don't do laundry on Sabbath and some days I just don't have 4 to do. I like those days!
use the clothes. Each night as clothes are shed I inspect them and decide to put them out for the next day, sponge off and dry for the next day, put aside for repair or replacement or if they can go to the wash. I am pedantic. Some people can't stand a messy house, I would prefer a slightly messy house and kids who are clean, reasonably well presented and comfortable. Smelly, messy kids in ill fitting clothing are not my thing! But if clothes are cared for properly, they can easily go two or even three wears. Limiting the wardrobe also makes it easier for me to keep track of the clothes. Laying out clothes the night before makes things MUCH easier in the morning.
store the clothes. Each of the kids has a basket and it is easy for me to tuck their clothes into the appropriate basket at the end of each folding session. Ironed clothes go in my wardrobe. Ironing is something I struggle to find time to do some days as I don't like doing it when the boys are up, but I do need to iron Jon's work wear and some of our 'good' clothes.