For years now I have been making my own autoharp strings (not the wound ones). I have several coils of music wire and a digital caliper, for measuring the string guage. The exact diameter is not required, merely something close, but not larger, than the original. I remove the ball from the broken string and re-use it. I make a double loop in the end of the string, so as to wrap the ball twice, and then spin the ball while holding the string and free end with pliers, so as to twist them together for about an inch. This method works well for me.

MD