I have a TS coop that is supposed to house 8 to 10 chickens and my 4 just fit. We had the same issue with the ladder so I put a brick under it to make it less steep. We also raised the roosting bars since they wouldn't use them, although mine still prefer to sleep on the floor.
I have a slide out tray on my coop as well, and had the same problem with shavings. I switched to sand and it works great. I scoop out the poop each morning with a kitty litter scoop and it helps the smell as well. My chicks were around 8 weeks old when I switched and they were scared at first...