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I've been lucky with Sheffields from that era. I've has some that were very hard but none that were so soft they wouldn't hold an edge. This article, here, on the 1903 Springfield rifle failures...

I don't strop between passes either. I would think that if you need to strop between passes your razor isn't "there" regardless of HHT. OTOH, it may just be that you don't need to strop in between...