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I'm honing ('scuse the pun) on this comment:

"...I did notice that they shaved a tiny bit better when they came back from honing, but not substantially..."

So, we can probably discount a...

So you strop one half of the razor, up and back, and then the other half? Interesting. If the edge is flat on the strop, that should work, I think, maybe. I don't use an X stroke, I just use 1/2...