I wanted to come back and revisit this topic because, like you at one time, the only real drummer in the world was Neil Peart. I remember being in jazz band in High school and my band director put on an Al Jarreau album(!) with the song Spain. I didn't know that it was Steve Gadd at the time. Later in life I began to explore music a little more and found an article on Steve Gadd's Spain in DownBeat magazine. As a challenge to myself, i learned to play the transcription in that article. Just the verse grooves alone are obvious but creative - typical of Steve. He plays the most obvious ideas and makes them sound incredible! He was outside the box before there was a box to be outside of!
What I would doif I were you, is to try to step outside of the boundaries you have set up with the "only Neil Peart/Danny Carey/Dennis Chambers/'insert name of your favorite drummer here' can play" thinking. It will change your playing in ways you can only imagine and take you further. I'm not saying these guys aren't great players. I am saying tke what you can from them and then go on, because Danny Carey is going to be playing the Tool gig for a long time.