Good points, Scooby-doo - that has been discussed on here before - KG, Ray and Paul getting together in their primes.
I was not aware of KG's intangibles that much while in Minny, but the way he played there I would not be surprised if even with the scenario you brought up a younger Big Three still making it work.
I think KG has always been about winning...I loved Paul even in his younger years, but it did not seem to me that he was ready to truly lead - up until he had that fateful meeting with Antoine Walker in the playoffs - on the bench - when 'Toine was urging him to play better.
I think from that point on - Paul really got it. I don't fault him for his immature years and his frustration, though - playing in Boston has got to be one of the hardest places to win in...just so much tradition. So much to live up to.
But I think Paul really got it, after that 'Toine talk.
Ray? I would guess he would change, too - but maybe not in the first season. In his prime he was so used to taking (and making) so many shots. I am lazy to dig up his defensive stats right now, but I'd venture to guess that defensively he would have to adjust, too.
We'd still need Doc Rivers to make it work....and a decent PG. And our center had to work, too.
But I think out of KG, Ray and Paul? KG would come the most Championship-Ready, IMO.