Dog digging troubles

In the flurry of housework and yardwork that kept me busy almost all day yesterday, there was an unprecedented amount of dog-dug holes to fill in. She'd done a lot of digging before the ground was wholly frozen I didn't get to counter last year, and then has been digging urgently since it thawed this year, while I couldn't do anything about it due to snow and ice, and then due to injuries.

Sometimes I wonder if I should bother. Our lawn being pocked with huge holes is not the end of the world. It's ugly, it makes walking around difficult, and it's a pain when mowing the lawn, but is it worth it to counter that by constantly filling the holes in only to have her dig more the next day?

On the other hand, the holes she digs under the deck alongside its support posts, or against the foundation of the house, seem more threatening. Maybe I'm wrong, but it seems like it can't be good to leave big gaps there. This is more certain in the back where there's a propane line against the wall; it's highly doubtful she could break the line, but it's certainly better to keep it covered.

This time, I found not only three or four places where the propane line was exposed, there was also in the front under the deck a trench against the house's foundation big enough that I could lie in it and be unseen from outside. That one was especially hard to fill in since it's under the deck with so little clearance I couldn't even sit up, which makes it hard to work a shovel or rake. (Especially with one still-sore knee.)

Dog trainers and books have very little advice about keeping dogs from digging beyond these two unhelpful statements: "don't let them outside unsupervised" and "keep them too busy to dig". So I'm working on ideas to keep her from digging in the particular places in question.

I am considering trying to put in hammer-in garden edging like what's pictured here, against the wall, hammered in at an angle so that the top edge is up against the foundation of the house. However, even if I get edging that can go in deeply enough, will she just dig to the edge of the edging and then pull it up? If I still have to go fill in the holes, I'm not sure if I've accomplished anything.

Another idea: dig up the whole area myself (and that's a huge, huge amount of work, particularly under the deck), forming a trench along the edge of the house about a foot wide and deep. Then I'd create a ribbon of wire weld fence the entire length of the trench, curled into a quarter-circle, so the top edge is horizontal against the house foundation and the bottom is vertical against the edge of the trench away from the house. Then fill the trench back in, effectively burying the fencing completely. Now once she starts digging she hits the buried fencing, and hopefully stops, but she can't dig up enough to actually pull out the fencing. I'm not sure if it would work, and gosh, but that's a lot of effort to do it.

Anyone have any other ideas? I really would love to not have to go fill in those holes at all. I could really use some ideas here.