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?

Heated ultrasonic cleaner may work

Careful heating of the body area, then light taps with a pin? Aluminum should expand faster than the brass and give it some room. the only issue I can see would be if there is still some thread on the bit stuck, that will need to be turned by something to get it out.

Edit: also could be damage to the seat area already from the over tightening of the screw, it says about 3 billion times in every manual and tuning section "DO not over tighten these screws" but folks do not listen read.

I believe nitric acid will dissolve the brass and leave the aluminum alone.

Aluminum and nitric acid reacts.

Al + HNO3 --> AlNO3 + H

You might want to try with a dental pic from the inside. Something you can lightly tap from the outside of the carb with small hammer. If you have a vibrating table or a way to vibrate the carb while you do it, it could help.

I just ordered a small set of mechanics picks so i will give that a try. So frustrating.

Might a robust sewing needle get it out?

I've poked several out with a slightly sharpened screwdriver. Heating the carb body first is recommended.