Sorry I'm confused. Does each mean something, I am not aware of, that would be osmething other than "every single one".
Because it doesn't seems correct to me.
I think you can say "His EVERY step brought more pain to him." (Although "Every step he took..." would sound far more natural) but I'm pretty sure "His EACH step..." will not be correct.
Yes, I'm happy to wait for further thoughts as well. As I said, I am not so comfortable with it myself. Here's [url=http://corpus.byu.edu] COCA[/url] and some other corpora.