nic - wow, that saved me a lot of writing, nice to have you here. Stick around, please.
My first reaction was that it was a pretty ugly looking slot, neither V nor U, and some nasty looking grooves and edges. No offense, Dave :-)
Nothing extreme about the break angle. Even if it is shot from the opposite side, the fat side isn't excessive and the G is less. Agreed. (Almost too bad, those ebony spacers are really quite nice...).
I'll also be curious to hear what TI has to say. I understand the concept of the uneven pressure on the windings, translating into stress on the core, but given how soft their nickel is, I probably would have expected the winding to fail. Curious.
As for files, it would be great to have a properly sized set of nut files, but they're pretty expensive. I have a 6 piece needle file set from a company named Gyros, that I bought at my local Orchard Supply. It includes a round needle file that I've used on both my bridge and nut. For a G string, you can only use about the last 1/2 inch of the file, but if you're very patient, careful, and do it under a magnifier it will work.
Your slot was apparently done for a larger gauge. That's okay, just focus on the half round that your string will sit in. I suggest filing parallel to the way the string runs up the neck, until you get a really nice clean fit as it exits the saddle. Then file the tailpiece side, following that angle, and finally smooth out the angle in between. Better to go a little wider and deeper on the tailpiece side, if in doubt. You'd like the string to be held firmly, half way around, just as it heads up the neck.
I might speculate that slop here could be contributing to the problem, because then the string would end up rattling around in the slot - but it's getting late for such heavy thoughts...
-Bob
(Dave - the pictures are just fine, really helpful.)