WELCOME TO THE CLUB........
Pretty much all of us have run into this.
I'll share how I have dealt with it. I use a small center punch with a VERY sharp point. I do an initial tap, straight down onto the screw head 2/3 of the way out from the center line of the screw head, and then angle the punch in the pit I just made and gently work the screw out. Each hit barely turns the screw, it takes patience, but I have been succesful every time I have done this (so far).
It is my personal preference since I hate the idea of drilling and trying to use an "easy out" since the head on these screws is much wider than the actual thread and I don't want to damage the carb threads.
The screws do not have any loctite on them from the factory but they do compress the rubber seal under the block so it takes a couple of turns to get them to spin freely.
As long as the head is not buggered up too bad you can probably reuse the screws, just don't crank them down as tight as factory. I have always reused mine without a failure yet (so far).
The problem you, I and many others have hit on is the screws in the Mikuni carbs take a JIS (Japanese Industrial Standard) screw driver that locks on solidly into the grooves on the head. Most "other" screw drivers do not seat properly and end up getting the results you have there.
Anyone else have a solution? Lets get this guy back on the water!