I absolutely love the mirrored idea with the coop tunnel!! Brilliant. I hope that idea helps you. If your current set up is movable now then you can decide if it might work in a better spot.
As for the grass, make them a garden inside the run. Make a “window frame” out of 2X4s with the flat side facing forward. Lay it right on top of the chicken run garden and cover it with chicken wire. If it is large you may want something underneath to support the wire a bit. It can sag some but you just don’t want the chickens to be able to scratch up theroots. I used an old bunk bed frame and the slats support the wire. I used hardware cloth because it was on hand, so, free. You can also plant something taller and surround it with a chicken wire cage. As leaves grow tall and wide they will poke through enough to be nibbled by your birds. Just remember to watch for sharp wire edges. When I made the bed frame garden I made the wire larger than the frame, put the wire on the ground, put the frame on top, wrapped the wire edges up and around the frame where I fastened it on what would be the bottom of the garden frame once I flipped it over. You can actually use anything for a frame as long as it is too heavy for chickens to move. That’s most things LOL. A hula hoop wouldn’t work

A window frame would. A bottomless bucket buried, leaving about 2 inches showing, would. An old ladder would be ideal! Just use your imagination.
have fun!