I, too, have repaired various phonographs and music boxes.  To remove
a broken spring from a spring-barrel, the easiest way is to whack the
barrel open end onto a piece of wood inside a biggish metal bucket or
a barrel.  It goes "bang" and out it is.  You can hold it inside a
thick towel or blanket if you want.

To get the new spring in you can just slowly work it in by hand or you
will have to get a spring winder.  Careful!  There is a huge chance
that you get it all in, but the wrong way round!  That is not fun.

Don't let it get away from you!  In case it does, it will expand mostly
outwards so keep your face out of that line.  It is best to do this all
outside as it minimises the chance of collateral damage.

Bernt Damm
Sydney