I agree with the posts above that suggest filling the hole with a mild steel rod and brazing it in with silver. The only thing I would add is that I would start the new hole with a "center drill". Google can picture what that is. They are designed so that they can start drilling a hole without the bit wandering off center. Regular drill bits will wander towards a softer metal side. Probably using a
#3 center drill that has a diameter of .246" (I'm too lazy to check to confirm). That is slightly larger than 6mm. I use my Bridgeport vertical milling machine so it is easy to place the bit exactly where I want and the mass of the machine keeps anything from moving during the process.