I apologize for not being able to get through this entire thread before responding to your photo, but I will get through the thread.
That's a nice coop and I don't think it matters much what is in the bottom if you're going to bend over it to pick up a chicken, it's going to stick to you. If it were me with this set up, I'd make sure there was a 1x4 or 1x6 or even 1x8 across the bottom of the door opening. That way the bedding would not come out and you wouldn't be touching any of it in the first place to stick as you lean over the top of it. Good luck. See y'all at the end of the thread.