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Well, this is a conundrum because I've had some of the same trouble with my wedges. I think it's easier to be heavier handed with the weight of a wedge.
Normally, I like to do about 12-15 passes on...

That seems a bit much on the linen to me and you could do more on the leather, but thats all MHO.
What about the tautness of the strop and a heavy hand, could these be responsible?

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You might be beating the edge off with your stropping. It's a common mistake.
Hold your strop very taut and strop very gently.
You'll likely need top touch up that edge.
How many laps do you strop...