I would never put HC on the bottom of the run. It just isn't a good idea when a 2' predator apron laid across the ground will do the job with no risk of the chickens feet getting injured by their natural scratching.
I placed my vertical supports 4'OC and ran 4' wide 1/2" HC from the top, down then spread it out 2' over the ground and pinned the outer edge down with HD landscape staples. You can then just let the grass grow through the cloth.
It looks like your setup is being built over a section of ground that has been dug out lower than the surrounding area. If that is correct, it is likely going to end up having rainwater and runoff pour into the area and keep it wet longer than it should be. Structures should always be built on high ground with the area surrounding it pitched away on all sides. Just like a house.