I have 68 trips around the sun for decades I have been raising chickensWhat does your dropping board, or similar contraption,
For years I have been lining my nest boxes with the folded empty nylon mesh feed bags
It would also work for your dropping board.
When a bag gets soiled pop out the soiled and pop in another. Poop just peels off in below freezing temperatures and just flakes off when left out in the sun to bake and dry. It is the best method I have stumbled upon in my 68 trips around the sun.
Oh! Remove the excess string from the open end of the bag it can get tangled in your birds legs and wings.

I have gone with a wire 2" grid (wire the size of a pencil) over my coop floor. Similar to what is pictured below with 4"x4"x4" cubed blocks stationed under neath the grid on top of a tarp to form a drop pit it worked excellent all summer and I will clean the coop before winter sets in and things freeze solid. The grid even keeps you chickens feet cleaner which in turn keeps your eggs and nest boxes less soiled. I live in Canada and am subject to -40º temperatures.
Easy Peasy Japaneasy.