Innsbruck the first day is no problem, as long as you get an early start. Innsbruck is great, I recommend the Hilton there.
I didn't go to Zurich, but it looks doable. Just get an early start, so you can take your time through the mountains.
I followed break-in to the book... but some folks hit the 'Ring. I say use common sense. You don't go very fast through those mountain passes, anyways.