Reading some in Art of Attack, it seems the h-pawn attack is a standard plan against the fianchetto castled position, so maybe a "wild ride" is just the way it is.
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In this article, GM Serper talks about the h-pawn attack against the fianchetto position. He says if you play a fianchetto opening you should be afraid. I have faced this h-pawn attack a few times recently and while I ended up winning, it was a white knuckle ride, not very pleasant.
So what's the defense against this attack? Usually I see it as white when I play the opening suggested by GM Seirawan, where you play Nf3, g3, Bg2, O-O, d3, Nd2, and play for an e4 push (mostly regardless of what black plays).
http://www.chess.com/article/view/edit--deletetypical-patterns-everyone-should-know-the-dangerous-h-file-part-2