Lots of good ideas in this thread, but I would take a slightly different approach. Get the carbs off and out of the way. Liberally soak the screws in Kroil and let them soak. The longer they soak with constant reapplication of Kroil the better the results. Get a small brass head hammer and "tap" the head of the screw(s) multiple times during this soaking exercise. You want to shock the screw as much as possible to help dislodge it and get the Kroil into the threads. The Vessel drivers are great for their intended purpose, but this situation will tax them. Best to go with a true hammer driver if you have the room for this. Don't go ape crap on the hammer driver. A little movement at first is better than twisting off the screw head or breaking the screw shaft. In some instances I have actually tightened the screw a little at first just to break it loose. Tighten, loosen back and forth. I can't speak to the interesting looking Vampliers as I have never used them, but what can work in these instances based on location and screw head size is a pair of small thin jawed Visegrip pliers, installed at 90 degrees to the screw head if possible. Just remember to work the screw back and forth at first, tighten loosen. Don't go for loosen all at once or you may not like the results. The key here is patience while letting the screw soak and tapping/shocking the screw but not enough to damage it any further. Don't think of this soaking period in minutes, sometimes it may take a couple of days. If this doesn't work the last resort is heat applied in a judicious manner and due caution, but that is another story. Good luck.
Rick H.