Grind whats left of the old stiud flush with the case , depending on your skill you may want to use a file rater than a linishing disc .
Once you have a nice flat surface arm yourself with a centre punch an " automatic one is best here " and indent the centre of the remaining stud '
With a steady hand and a sharp 3mm ish bit pilot your first hole a perfect right angles to the head through the stud , some cutting compound or copper slip will help here " slow and constant pressure "
Increase this up till 6.5 mm hopefully you wont of skidded off to one side into the head , with an 8mm tap re-tap the hole .
You can now re-place your stud , I personally would flaten the thread a bit towards the top of the thead to bind it into the hole a little and use a bit of green loctight .
Simples