Thanks for the answers ya'll. While I do appreciate the additional alternatives presented here, I am definitely looking for a physical digging barrier. We live in a semi urban area, so while most of our digging predators are nocturnal, our main run must also be a fortress from above and below. We have hawks, as well as the occasional loose domestic dog(probably the biggest risk honestly). Our neighbors just lost a hen to an under fence break-in around 4pm, and we wouldn't like to see the same thing happen here. We will have a larger, lower security area where chickens are only allowed while we are in the garden, but will want our main run to look something like this:
Chicken Winter Greenhouse
Electric fences sound great in theory, but seem to require disciplined vegetation management outside of the chicken destruction zone, and to be honest, my partner and I have discovered that's just not who we are... plus as Andrew Mayflower said.... weasels? The chickens my parents had when I was growing up were all murdered by one in spite of the zippety zap.
We do plan on raising the coop off the ground for moisture reasons, but think the under coop area would be a great place for the chickens to find shade, and perhaps dust bathe as it will be sheltered from rain and sun, so we will want it enclosed as well.
Our space is a little small for a movable coop, plus we're pretty intent on being able to stand inside the coop... to keep us honest about the conditions our birds are experiencing.
I think we might go for different solutions for different parts of the boundary in the end. Burying rocks downward around areas where we need to minimize our footprint and out in others, perhaps resorting to the hardware cloth if it proves to be too much work.
I must wonder though, when people use hardware cloth do they make a point of replacing it regularly? I would be worried that it would eventually be nonfunctional and I would have no idea until I lost my entire flock to someone's escaped dog who wasn't even hungry. I suppose the poky bits left behind might still be a deterrent, but this really isn't the type of legacy I want to leave, and I've certainly been willing to scratch my hands up when I was determined for one reason or another.
Either way it's been great to discuss some finer points of predator protection with ya'll. Thanks especially to Andrew. Descriptions of real predator behavior was the main thing I was looking for. I imagine domestic dogs would behave somewhat similarly to foxes or coyotes in that situation as well. I wonder if they would give up sooner because they were less motivated by hunger, or later because they aren't as worried about wearing themselves out and not being able to catch their next meal. They also probably wouldn't be as afraid of humans if they had never killed a chicken before.