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Thickness of the wedge does depend on the grind though.
If you have a larger razor, and you want to blade to close to a position close to the spine, a thin wedge will be too thin.
The wedge should...

Actually, wedges are wedge shaped.
If there is a bit of space between the point and the wedge, The wedge can be a bit smaller because the scales get futher apart when the distance from the wedge...

Repeatability is only worth something if you make the same razor multiple times.
Otherwise, each one is different. I just eyeball it and adjust as needed.