Here is my first reaction and posted without any thought, so take it as that.. Why not just use loop ends and not balls? Take the peg end of string down through hole in tail then up through the loop and then to the peg. The string is captured.
And just for information, I purchased a pack of 20 normal tail cords from china cheap. A couple of them failed when tensioned, leaving marks on the violin. The cords FM sells is higher quality as you would expect. They do not fail. Further, everything FM sells is that way. He has done the tedious work of finding the good and passing the bad.
My FM soloist has FM strings, FM shoulder rest, FM boxwood tail, FM tail cord, using FM carbon bow and it should have a FM chin rest,,,,but we are all waiting on that one. hint hint.
It has been fun working on my cheaper instruments, knowing that if I mess up its not life changing and it is also fun looking for bargains, but when it comes to the better quality, we here always head to FM.

When I was traveling in a rock band I made a practice set of drums using plumbing pipe, 3/4" plywood with rubber tops for drums.  Everybody appreciated my efforts.  No one wants to hear a drummer practice.

On your violin and cello you might want to consider glue on the sound post and bridge, or even cut the bridge tall enough to make holes for the string to pass through, that way the bridge is always captured.