I'd do more than revamp the evergreen cards. I'd completely redesign a class or two. I hope those are the "big changes" Blizz has hinted at for next year.
That's more or less what I meant, though. A lot of the RNG effects are in basic & classic too.
For example, here's some concepts for I wrote up for the druid class. (I've done a whole document with almost every class and most of the tribal cards, but I'm not sure how to safely share it).
For one thing, like modern sets, the classic set should probably have two legendaries (likely for two different styles of decks).