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Looks about perfect. If I'd made one it would look like that so it should be fine. A pipe cleaner with brake cleaner or a .22 bore brush before installation in the firing pin channel should help.

I saw that Jack First ad, you have the measurement right there... It would be trial and error anyway, start long and work down. No broken piece is needed other than the ones you have. That gives...

Working with the pieces you have and the gun itself, I'd use a piece of a drill bit shank and make one. You can precision grind the tip to shape with it chucked up in a drill or a lathe if you have...