Ahhh, some of my most-played stuff. Thank God for the empeg - I was on the 3rd taped copy of Surfing With The Alien.

I was wondering the very same thing last night. I didn't come to a solid conclusion. Some of Vai's work could easily fit in some of the definitions you've found - his Zappa influence can clearly be heard thoughout his career, and he is by far the most imaginative, and creative of the four, and takes the biggest risks with his music.
Satch could fit as well, but he is more often put in the equally misunderstood Fusion category.
Yngwie? On the one hand, he is neo-classical, complete with church-organs and mythical themes, so fits better than Vai or Satch into the 'typical' 'prog' category, but on the other hand there is little progression over his career IMO.

Did you know that Yngwie was in a bad road accident in the early-/mid-80's and was told by doctors that he'd never hold a cup of coffee again in his left hand? He reckoned that he'd got 95% of his playing ability back. I'd be happy to have the other 5%