Will disassemble the diff again and have a good look, but from the external view, it doesn't look like its an internal separate shaft.
And if it was pressed in from the other (internal) end into a blank hole, I wont be able to press it out. But will look for and respond again.
As you have nothing to loose, before replacing a weak designed part, I'd attempt to modify / fix it.
To remove the broke part, either drill the plastic, put a sheet metal screw and yank it out or simply melt it out.
Now the fun part. Find or have machined an identical "rod" that fits snug in the NOW open hole. Some RED Loctite will keep it from moving (remember, it was just plastic before). If that rod is a "standard dimension", even easier-cut to length, clean up and install...