What on Earth do you sharpen those things with? The only triangular file I own that could possibly be up to the job is a Vallorbe Valtitan (Rc72, $25 each). Are there other options besides that?
I have some solid WC flat files from my days of ski racing, and I have no doubt that one of those could cut Rc56 steel, but AFAIK they don't make triangular files like that.