Facebook way != normal way
I've done a little more research on this and this problem has tripped up a lot of people. It occurs for example when you switch a site from http to https. You can fool FB by having your og:url meta tag and the url fed to the FB code snippet both point to the old url, but then you are forever getting likes and FB comments against those older urls.
Actually, it gets worse. Based on the research I did, I thought I could work around this at least for the album pages by setting the og:url meta tag to the old url and also setting the url that is fed to the facebook code snippet to the old url. It's the album pages where most of the likes are. I also wrote some code to do this just for older albums, so that I wasn't tied to the old url structure permanently for new albums.
When I tested this it worked! But only once. The first time I visited such an album my likes were back. Visit a second time and more and they're gone. Wiped. How is this possible? I guess you really do have to keep the old site still live with redirects for this to work. This is insane. As you say, I'm out of luck. Completely.
The 'unique image' idea floated earlier isn't going to help. My main problem is albums, and the URL change for them is from www.mysite.com/album.html to www.mysite.com/album/ and nothing short of a deep and ill-advised code hack is going to help solve that problem. If I hadn't done that silly album URL rewrite then I'd have no problems now. Groan.
My original post was about rewrites and redirection. I've got that working now. I've created some rules in htaccess that are working well. So there's no pressing need for 'unique image', as it's not needed for redirection, and it isn't really needed in practice for FB likes. Unique image would solve the FB like problem for me on image pages, but image pages aren't the main cause of that problem, so the practical benefit would be negligible.
That said if 'unique image' ever gets implemented, I may well use it.
The end.