No easy outs....
No, the easy out idea is out of the question. I tried that. It didn't work. When you get a bit in the bolt, the only easy out you can use is a small one. I broke it, then, when I tried to go one size up, I expanded the metal when I tried to turn it, that it just made it worse.
What I don't understand is, with this problem being common, how come Mikuni hasn't made the stud pass through the carbs in an open style set up. They could cast the top and bottom with 1/2" ringlets top and bottom, the bolt shaft could pass through, leaving the majority of the shank open to the atomsphere and exposed from the side!
It looks like your easiest way to start on this would be to remove the rotary plate. But even then, your most likely to run into seized bolts there too!
If I was at a point where I had no other choice, I'd use a dremel tool (angle type) with a cutting wheel and cut gently into the side of the bolt between the carb and rotary plate (you only have to cut one). The depth of the dremel cutting wheel is about 1/16". I'd try and stay off the plate and cut into the carb side, as flush as possible with the carbs bottom. If you look at the way the carb is sealed, this small cut should not affect the sealing of the gasket at the throat of the carb.
Once off, you could work the bolt out. I worked mine out over the course of a couple days, soaking and taking another bolt (expendable) and tapping it out. You tap till you move just a tiny bit, flip the carb and do it from the other side. Then, soak. You'll have to do that often. The stud will move further and further each time you tap on the bolt from front to back and vice versa.
Good luck!...... your gonna need it!:cheers: