MinnFlyer:
With my soldering skills I'd be afraid to use that much heat back there around finished pieces.
How about using JB WELD instead. Also, back up with some wire and, cut a little notch in the center of the brass tube so the JB WELD can release out and key everything together. The brass tube would go the full distance between elevator halves about 3/4"on the SE. It's really the angle(skarf) cut that mechanically keeps the rods turning together.
Cutting the rod could be a bear with a hacksaw. Make a square stick the dimension of the distance between elevator halves and about 7" long. Chuck it in the vise standing up. With the hacksaw cut down from corner to corner the depth of the blade. Cut a slot for the elevator joiner wire in the center of the stick. When you put the elevator assembly in and pointing down you should be able to get a good clean cut without any danger to the elevator assembly.
I know it's just a "matter of time" until I'm going to have to try my own advice!