Try chucking a short length of guitar string (5th or 6th) in an electric drill and work it down through the fitting. Just cut the end; don’t try to polish or protect it.
Any wire-wound musical instrument string about .06" or perhaps a bit less in OD should work.
Caveat: I have not done this, but I have used a guitar string for something similar. You may need a guide tube or an extra set of hands to keep the string from twisting up before it enters the fitting.