Ideas to get cat to stop “burying” his food dish?

My cat is one of those cats that feels the need to bury his food bowl. Doesn’t seem to matter if he’s got leftover food or not.

I realize it’s an instinctual thing, but he’s just flipping over his dishes now. Tried switching to classic dog-bowl-shaped dishes: he can get a claw under there or something.

And what’s worse is he knows I don’t like it, so as soon as I get up to correct him or something, he hears it and leaves. And if I don’t get up he’ll just go and go and go. So I’m having trouble figuring out how to even try doing something about it. He hears the floor creaking and knows right when to stop. It makes it all extra annoying because you know he knows you don’t like it.

Any ideas? Seems like my only option is to make everything unflappably somehow.