But, I found out that nylon strings in general, both trebles and basses, are more likely to break when secured by a ball-end than by being tied in the traditional manner.
I found this out by switching back to the Pro ArtÃ© strings but tying knots at the end of them and using the knots as ball ends. I never had a problem with them breaking before, but when secured by only a knot end, like a ball end, a few of them broke??the strings broke, not the knots. The breaks have so far been about a centimeter from the knot or ball-end. (I made 'double overhand' knots, which are simple 'stopper knots', which are big enough to not go through the hole. I marked the slack ends of the treble strings with a sharpie to measure any slippage, and there was none. Again, each knot was still a knot after the break.)
To protect against breakage I now wrap the treble E and B strings around the bridge block so the string goes through the hole twice. Unfortunately the holes are too small to do this with the other strings. For those I'm thinking about making a tight fitting sleeve which fits over the string and in the hole, to see if that helps.
These are those right strings. It took going through a lot of different sets to find the strings that'll bring out what this guitar has to offer, but once we got here, the match was instantly clear. If you have an older classical of this sort - not ever top quality, but competent, and improving with age - and if you suspect it has more in it than it's been willing to tell you, try this set. It might be exactly what you need.