Hiya Steve, :)
My first thought about your specific problem, of breakage just before the peg, was that if the nut slot was tight / binding, it may be not allowing the whole string up to tune, but rather that when you get past D- D# , the string has lodged so firmly in the nut slot that you are only tuning up the last 2-3cm of string and that snaps before you hear the rest of the string go up in pitch ?
I also wanted to confirm that with D'addario ( just in case the top 'E' of the GHS comes out of the same generic factory ) the top 'E' on any guitar kept breaking on me also. In my case, it was always the high 'E' - when I had released the tension for fret cleaning e.t.c - and then re-tuned up to 'E'. In my case however, they seem to unwind themsleves at the ball end.
For Jazz , where I am using 12 or 13 in standard tuning for my top 'E' - I just had to make sure that any spare 12 or 13's I had ( beyond Thomastiks own excellent and resilient top 'E' in the packet ) - were preferably Newtone , or at a pinch Ernie Ball singles - but NEVER D'addario.
Due to 'Flashbacks' caused from memories of winding D'addario singles ( of 12 or 13 gauge ) up to tension, I am still bracing myself, turning my face away - and clearing the area of cats before I go above D - D#
- with any string. I must have P.D.S.D - ( Post D'addaric Stress Disorder ). :)