Douglas black wheels are anodized, not powder coated, so the finish is not the problem. Some older VanK and Outlaw wheels that were powder coated on the insides had issues, but never saw a black Douglas be the cause of a tire coming off the bead.
You say that the tire itself is 1/4" shorter and significantly softer? I don't doubt that with the way your kart has been mishandling/hopping, that it is breaking the sidewalls down over time as well. That might explain the "softer." I'm curious about this "shorter" though. Most Vegas mount up 34" - 34 1/4" C on a 10" wheel. The wheels aren't a different width by chance are they? No bends (or out of roundness) in the wheels? I still suspect the tires didn't bead out originally. As others have said...Vegas can be some of the toughest tires to mount; heat, high psi, etc.