Or just make the whole page rotate

    body[href*= "<OFFENDING URL>"] {
      animation: rotation 20s infinite linear;
    }

    @keyframes rotation {
      from {
        transform: rotate(0deg);
      }
      to {
        transform: rotate(359deg);
      }
    }

We're trying to punish the people running the proxy mirror, not the users who stumble upon them just trying to use the site

You could look at it as trying to get them blocked by search engines. Can you detect when they're proxying a search bot as opposed to a user? As for punish, you don't have to make it eye-bleach, just enough to make it firmly NSFW so nobody can get any business value from it, or even use it safely at work.

A little soft NSFW would also greatly accelerate them being added to a block list, especially if you were to submit their site to the blocklists as soon as you started including it. You can include literally anything that won't get you arrested. Terrorist manifestos, the anarchists cookbook, insane hentai porn... Use all those block categories - gore/extreme, terrorist, adult, etc.

In that case, write some JS, that wanders around the Hubble site, randomly downloading full-res TIFF images for the background, or that randomly displays Disney images.