What you've done looks fantastic! I wish we had that much space and such a beautiful setting!
Critters will go as close the the run or fence as they can to start digging. They are smart, but not smart enough to think, "Well, ran into a barrier here - maybe if I move back a foot or two away from where I really want to be I can get in -- or out." Our ground was way too hard and rocky to dig a trench and put in hardware cloth. Besides, I'm way too lazy for that much extra work! We live in town and my set-up is visible from the street, so whatever we did build-wise and protection-wise had to be either invisible or attractive.
We used the long roll of single strand wire designed for electric fences and cut off a piece about 5 feet long to use as "thread". Then we literally sewed hardware cloth going about 2 feet up the sides of the run, repeating the thread cutting for lengths as needed. Any longer than five feet and the cuss words were released as it tangled up. Any shorter and it would have taken forever. At the bottom we folded the hardware cloth outward, forming an apron, and tacked it to the ground with landscape fabric staples. Our rolls of HWC was 4' wide, but you could do the same thing with 3' wide, going up the run about a foot and then out 2 feet, or even chicken wire. All you are trying to do is form a barrier that prevents digging. By golly it worked! Our birdy English Setter, Molly, got so overexcite when the chickens were released into the run for the first time. First she paced the outside of the run, then she got to digging. One broken and bloodied toenail later she decided those chickens just weren't worth it and she's never done it again. Same scenario with a neighbor's dog, just this morning, in fact. He jumped our fence and was trying to dig under the south side of the run. He didn't get anything but sore toes and a thrown rock to the behind.
Our initial plan was to cover the hardware cloth apron with flat rock. But it showed it's effectiveness immediately even without the rock. And the grass quickly grew up through it, which allows Ken to mow right up to the sides of the run without hitting anything. No tall grass around the run means no hiding places for little pests, either.
By the looks of things the last thing you need is advice...you sure have done an amazing job and I'm a little envious. But I just thought I'd share what we did to deter digging.