Well back to these broken post screws.
Drilled new holes next to broken screw - Not happy -Post inprint showing where post was.
Tried to find one of those Dremel diamond engraver bits - Couldnt find one.
So last resort - Remove the broken stud - This is what I ended up doing (Picts attached) and was quite happy with the result - Its also a bit quicker.
1. Mask up - in case drill slips
2. Drill little holes around broken screw.
3. Tap broken screw side to side,back to front to loosen up screw (Try not to do too much damage) Remember post will hide any butchering.
4. Grab the top of the broken screw with circlip pliers (Small and strong) and unscrew broken screw- Toss it on the floor and swear at it.
5. Get the smallest length of wood dowel, cut to length,drill out hole to same dimension as dowell.
6. Apply wood glue and stick in hole, redrill new screw hole and thats it. (If youre bugged by the damage around the dowell,fill it with wood filler,dont forget the post will hide it.