TOPIC:

Mixture screw got so fubared beyond reach

I really tried to finesse the screw outta there without damaging the hole, but to no avail. 

Here's what the carb body looks like. The black overspray was none of my doings.

Yup, that's what i thought as previously mentioned. I don't think the 82 1100 Spectre had painted carbs but i know the 750's did. Have You tried to center drill that brass screw out yet? If You have noteworthy NEVER use a conventional twist bit!!! If you get half-way down the center the brass will bottom out with force and mess-up that tiny hole you are trying to expose, not to mention jamming the sharp tip of brass in mentioned hole and breaking off. Use a Left-Hand twist bit only. Now that said, i do these all the time. Would be nice to retain what you have already since that appears to be the only, common, issue.

I recommend drilling into the pilot screw, making sure you are dead in the center.  Start with a small drill bit, and move larger after making sure you are centered.  The goal is to create a centered depression, maybe 1/8" deep or so, so a torx bit can be hammered into the hole.  Before doing the hammering part, use PB blaster on the screw, and torch the pilot tunnel, to heat the metal.  Don't go all gonzo on it, but with a tight fitting torx, you should be able to work the old pilot screw out.  This has worked for me in the past.

Another option, take a thin dremel cut off disc and cut down into the pilot screw tunnel, and create a new slot in the pilot screw.  Once that's done, find a screwdriver that affords a tight fit into the slot you just ground.  Grind a larger screwdriver as need be.  It's critical that the screwdriver fits tightly.  Then heat with a torch, spray PB Blaster, and turn both ways until you get screw movement.  Then it's back and forth.  Spray the blaster.  Back and forth.  Heat, back and forth.  Slowly work the pilot screw out.  Hopefully you won't butcher the screw slot you created.  Most of the time this works.  

Yep FUBAR'D

I did end up getting it out, but man I went full tilt on it where this is not an item to really do that with. 
Now, the small pilot hole located inside the throat was elongated just ever so slightly. 

sorry didn't mean to mob this post