If its under warranty, let your dealer handle it before you go cutting and welding ,as once you get to that point your not going to get it fixed under warranty if you run into problems.
But if you insist on trying it to repair your self, would it be posssible to drill a small hole in the collar on the shifter but not into the shaft. Maybe towards the center to get some pentrant oil to the middle or posiblly grease pumped in?
^^that's what I would recommend