One more thought----It sounds like your pups are forced to live on multiple layers of padding and materials. Give them a bare floor options, and watch all of them take it. They need the choice.
I'm not sure how much you are willing to change since this works during the daytime for you.
I currently have 10 pups which are 7 weeks old. They spend much of their day in a 9 X 5 foot wide "laundry closet" surrounded by 2 puppy pens with bifold doors open to the rest of the house.
They have a 3X3 foot rabbit tray with horse stall pellets in it where they potty. When not out with us,they play in their area and potty in the box. I change the stall pellets first thing in the morning and right before bedtime. I sprinkle fresh pellets over waste during the day. They do sometimes stand in the tray and poop over the edge which I pick up with napkins and put in a garabage bag which is stored closed on a nearby shelf. I empty garabage frequently. I make the area small to sweep one side and then the other to avoid broom chasers - we do this 2x a day.
I wake up in the morning to a potty box which is easily dumped and maybe 1 or 2 poops to pick up outside of the potty box. Not a big deal and not very smelly at all.
Mine also go outside for feeding times/potty weather permitting 3x/day.
To me, allowing pups to potty on layers of fabric, rugs, etc. teaches them to potty on the carpet and furniture later.
I buy linolem from Lowe's and cover my floor with 2 layers. We have a small room (12x12) and the puppies have the entire thing with an expansion gate across each of the 2 doorways. The whelping box and my sleeping couch are out of there by the time the pups are 3.5 weeks old. We have thick layers of newspapers in one corner and lots of bedding and toys in another area. We changes newspaper first thing in the morning and throughout the day. They go on the paper pretty well right from the start.
I don't think a whelping box is for pups after 3 or 4 weeks old.
At about 3 wks, I convert my 4 X 5 foot pen to a 5 X 10 foot pen I use one end for papers and the other a Kuranda bed and a blanket they take to going on the papers very quickly
also, at 7 weeks - they all start to be crate trained if I have room - 1 pup to a crate, if not 2 pups to a crate amazing how quickly they learn to hold it til AM
