Need help getting broken mixture screw out

I got a used set of RS 36 carbs, in cleaning them i realized one of the super small tips of the mixture screws has broken off inside the carb body. The hole is TINY, and i believe it is tapered so that the corresponding taper on the screw can fit it, so I cannot drill it out. (plus i don't have any drill bits that small). I tried pushing it out with a push pin but no luck. You can see the gleam of the brass in the hole where it broke off. Pretty pissed off right now, these were not cheap. How can i get this out without damaging the carb body?
EDIT; sorry about the wrong section

Hey Doc, I'm sure you are not using these right away? But don't rush it. Get some ideas first. I soak all my brass carb parts in the metal prep & etch rust remover stuff (phosphoric acid) it cleans them real nice. Put a drop or 2 into and soak it for an hour. Blow it out. Then freeze the carb in freezer, might retract enough to push out from the outside hole. (freeze it like bearings)
I have some small implements and a finger twist drill that is 50 years old. I use that drill bit to drill out front brake master cylinder holes.
it's early here, I'll post a picture in a few hours.

I found the same thing in one of the carbs when I first got my bike. I never got it out and messed it up trying tho. Think I ended up flattening the tip so it had no chance of pushing back out. In the end I bought another rack.
If they where  a nice  RS rack and the chance of permanently damaging the mixture screw orifice is high  I think I would send them to someone who has experience in this problem.
The  link below maybe of help

kzrider.com/forum/3-carburetor/605125-lo...body-for-rs36#754365

This may help... members.dslextreme.com/users/cbsaunders/...ot_screw_removal.pdf

Also this... members.dslextreme.com/users/bikecliff/i.../vm_carb_rebuild.pdf

z1kzonly wrote: Hey Doc, I'm sure you are not using these right away? But don't rush it. Get some ideas first. I soak all my brass carb parts in the metal prep & etch rust remover stuff (phosphoric acid) it cleans them real nice. Put a drop or 2 into and soak it for an hour. Blow it out. Then freeze the carb in freezer, might retract enough to push out from the outside hole. (freeze it like bearings)
I have some small implements and a finger twist drill that is 50 years old. I use that drill bit to drill out front brake master cylinder holes.
it's early here, I'll post a picture in a few hours.

Here is the pic. twist drill is .040".  Twist drill Made in Germany. All old school from my Dad, who I lost in 1972. Very sentimental stuff!

Very cool. Looks like that curved one might do the trick.
Steve

unfortunately the hole is offset so i can't push at it straight. I called Sudco and they had no solutions for me other than swapping the carb body out. I bought a small set of mechanics picks I will try that.

Heat cycling might loosen it a bit.  Assuming brass and pot-metal expand at different rates, they should deform each other and loosen. 
It could take many cycles and the pot-metal likes to melt suddenly so don't get too hot.

Pushing too hard can make it mushroom and will then become a rivet with no way out.

How about drilling a hole on the opposite side 180 degrees around on top as close to the body of carb. Then you could have a better, straight line shot at it. Then just weld up or epoxy that small hole.

loudhvx wrote: Pushing too hard can make it mushroom and will then become a rivet with no way out.

That's what happened to me

Did you give Randy's Deburring a call

found a shop in California recommended by mikuni themselves.
Randy's deburring.
He quoted me a cheap price.
He told me They have great succuss with people who overtightened the screws and break the tips off in the body.
They have an edm system for that.

I'm gonna do a heat cycle and give it one more try before I send it out. Randy's Deburring quoted me $75 plus shipping. That seems reasonable for the amount of work it requires.