Those are all excellent suggestions, and I know for sure because...I've already tried all of them (repairing colour profiles was new to me, glad I learned about that, and checking for a clogged nozzle/low ink was, embarrassingly, one of the last things I tried).
I've even re-profiled my printer for this particular inkset and paper. This got rid of most of the tint but, amazingly, there is still a bit left. I'm genuinely confused.
Thanks very much for the very good advice, I do appreciate it. To solve the problem, I had to boot into my emergency Snow Leopard drive (a mirror of a long-ago upgraded startup disk, running CS4) and print from there. That at least tells me it's a software problem, but I haven't yet determined if it's the OS, or Photoshop.