Since you have access to a stick welder it's easy - really. I didn't believe this would work until I did it. Doesn't matter what rod you use, but use a larger diameter vs smaller rod. Turn heat down. Stick 2 or 3 rods together end-to-end by welding them. Once you have a long enough piece, cover it all except the end with duct tape (this step is important ). Ground the carrier, and weld the long rod to the broken stub. Pull it out.
Yes, it really works quite well as long as you turn the heat down so the rod will simply stick and not strike an arc.
damn I wish I would have tried this before I gunked it up with jb weld and urethane. Both of which didn't work so I am going to dig in tommorrow and try getting the carrier out.