You could make a page that shames their domain name for stealing content. You could make a redirect page that redirects people to your website. Or you could make a page with absolutely disgusting content. I think it would discourage them from playing the cat and mouse game with you and fixing it by getting new IPs.
Assuming you've monetized your content with ads, depending on your ads provider, this may have deleterious effects on your account with that provider, as they may then assume you're trying to game ads revenue.
That's my read on it anyway.
Not if you value the people who might move to the real domain.
Love the idea.
E.g. you'd like some way to redirect people from $PROXY site to $REAL site, and disgusting content on $PROXY won't do that - it'll reflect poorly on $REAL
edit: or when somebody embed-links your image inside some forum, replace the original filename with the contents of hello.jpg