At one of the plant nurseries here they have a chicken coop in the back with those type of nests that you are talking about. They are covered with old pieces of carpeting, the boxes have a gentle slope, and the channel for the eggs is also lined in old carpet.
I guess they just change the carpeting from time to time in the nest boxes. Old carpet is not hard to find for free.
Have no clue on the percentage of slope of the bottom of the nest boxes, the egg channel is built out from the rest of the coop, much like you see nest boxes built outside of the actual coop. The egg channel runs the length of nest boxes, and all the boxes "dump" eggs in the one channel.
If that makes any sense at all without photos.