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No, just the climbing buttons. Like you, in cross races I'm on the hoods most of the time so didn't feel the need for additional shifters. That said, I have climbing buttons in each shifter and, as it's a single ring set up, I've set them up so both right hand buttons shift up a gear and both left buttons change down.
I started with a single button, but in the heat of a cross race, when you're going cross-eyed from the effort, working out which button to press to change gear was challenging.
Awesome! with the sprint shifters too?