A foot is nothing for a bird to jump...once they get used to it.
Sand stinks....literally.....mixed dry plant matter(browns) is the best for 'eating' the poops.
Here's a great description of contents and how to manage organic 'bedding' in a run or coop...and there's a great video of what it...
The way to get the cockbird to sleep inside is to have a large enough coop to lock them all in there for a week or two.
The high door is to keep deep bedding from falling out and/or impeding the door swing.
Does the 6x20 run have a solid roof....a mesh roof??
What is your climate/location?