Poop board...

I wouldn't use the 1/4" inch stuff. I think 3/8 would likely be adequate if it is actually 3/8" thick. Err on the thick side, you won't look back and think to yourself "gosh, I made that poop board *too* strong, I wish it was thinner". You will only regret making it too thin. I would also recommend using exterior grade plywood.
It also depends on the dimensions of your board and how it is supported. Mine is is 2' by 6' and is supported along its entire perimeter by 2x4 rails attached to the coop walls. I'm sure mine could hold 300+ pounds without issue. The plywood I used is 7/16" by actual measurement. It is plenty strong and easy to work with. It is in fact more than strong enough which leads me to think 3/8 would be adequate given strong support along both sides of its long dimensions.

 

I jut made a 1 1/2 x 6 foot one with some left over 1/2 in smart wood covered with linoleum tiles. It's screwed into the 2x4 coop framing. So far so good, but I don't have any added weight in it from PDZ or sand.

 

Poop boards should be located higher than your nest boxes an preferably the highest spot for roosting through the night.
I have my 2x4 roost 3½ inches from my poop board.

I find the spacing ideal it saves the day when eggs are laid through the night while they are roosting.

I have my roost in cups and can just put them to one side when cleaning the board.

In my nest boxes I fold a feed bag to fit (nest boxes are 1 ft³). When a bag gets soiled; fold a new one; pop out the soiled; pop in the new.

Easy peasy!.

Chicken coop is salvaged 4x8 metal shed.







My roost over my poop boards is very similar to this photo (except my roost are resting on the lower 2x4).
I recently friction fit a piece of vinyl flooring over my poop board.it makes clean up even easier; Pop out; Scrap; Hose; Pop in.

Winter months even easier flex over compost bin DONE!

Easy peasy!. My poop boards are just thin veneer works in my small 4x8 coop.