Welcome to the flock! Quite a playground you have for your girls. Buttercup reminds me of Agatha, my EE who is currently sitting on 15 eggs. Fine time of year for chicks here in Wyoming, I know, but it is what it is and I have no intention of disappointing my 8 year old granddaughter after the time and fretting she's gone through for "her" chicken!
I would strongly second the advice of putting to good use the hardware cloth you have. We ran it up a couple of feet on the run, then folded it at the bottom and extended it out about 2 feet as well. We tacked it down with landscape fabric staples, intending to put decorative rock around it. Yeah, about that word "intending"! As it turns out covering it was unnecessary anyway because the grass grew up through it quite nicely and it can't even be seen now.....hubby Ken can mow right over it. We know it works well. The first day we turned the chickens into the new run our English Setter, Molly, tried to dig under and broke and bloodied her toenail. She decided they weren't worth it. Don't just think in terms of the bigger, more obvious predators,either. As far as this old lady is concerned any system that deters mice is worth it's weight in gold.
Good luck with your chickens....and it's nice to meet you!