Yeh, that's interesting. Mine is the 22BR Remington Redding type S FL resize die. Mismarked from Redding maybe?
Funny you should mention that about step sizing. I used to do that for the first year. Then I shot a match with a guy running a 6BR with Norma brass (I use Lapua) and I ended up with some of it mixed in with mine. I run a progressive loader, so his fed down and got resized, I felt it was stiffer on the press, so pulled them out and caught the error every time I got one. I remember that I resized and pulled out like a half dozen of them. And looking at them later, they resized perfectly in one pass. That was the last time I stepped them down.
I've probably resized 500 or 600 pieces in one pass now. It works just fine.