I recognise the problem (in the UK I was based in Shepperton, with the Watkins works nearby in Chertsey...). It would seem that the ball-end windings don't like the exit from the saddle. As an experiment, try passing a new string through a spare ball-end (you seem to have a few..!), such that the ball can't sit so far down in the seating. This may keep the twisty windings further down, so not on the break angle. A 2BA nut could work, too (you're of an age to know what a 2BA is, no..?). My second recommendation would be to try another brand I use Elixir, but used Fender Bullets for years; they have the ball-end 'slug' moulded into the string, so no twisty bit... If you're married to 9's, that's fine, but they're easier to break than 10's; try upping the gauge, to see..? Report back with progress, successful or not, please..?