Need Hinge Pin Replacements

You're right, that 5/16" is a little too large for Emco storm doors, in my experience. I recently repaired an Emco storm door for the Lutheran Church in my neighborhood, coincidentally, and what I ended using springs and bushings from the 40-165 kit in addition to the metal pins from the old hinge, and I had no issues. If you mix and match them like that I think it will work out fine.