I've seen pics of your setup (unless I'm getting you mixed up with someone else,). It's fantastic!
I really think it depends on the chickens.
My chickens roamed far and wide. I couldn't see them from the house, they crossed the road and were nearly hit twice (that I saw) and would parade right down the middle of the road and march up the hill.
On vacation in DE we drove past a lovely flock of SLW scratching around the yard. On the way back to the house we drove past a dead SLW laying at the side of the road.
I too think the dome is cool but would never spend that kind of money on it. I have about $2500 into my entire setup including coop (converted shed), a 28x12 run with 16x4 annex off the back solid roofed predator proof run attached (built from scratch), three lengths of 164' x 42" high poultry netting that enclose 1/3 acre of well planted grounds, 10,000-volt charger, fence posts, gates, chicken supplies... everything. I have housed up to 30 birds. In the 3 years they've been in this setup, I've only lost one young pullet to a hawk. The grass is green and they are happy and that makes me happy and therefore worth every penny.