You can solve the problem in two easy steps: When your front foot is below your back foot take a normal stance with a “centered” ball position then move your lead foot down the hill and tilt your shoulders with the slope (see the photo below). Setting up this way delofts the club so use a higher-lofted wedge.
This is not where you want to be especially during a major. To prove it I threw six balls into the grass in this area during my fall visit; the photo at right shows the only time I was able to lash the ball onto the green (and it eventually rolled off the back).
Of course my personal answer to the original question is “Yes I listened.” I obeyed what the slopes crowns contours wind green firmness and speed asked of me. I’ve been around the game a long time yet Shinnecock always teaches me something new.
Having the “touch” in your mind’s eye to know how firmly to stroke a putt (so its speed matches the break) and then also having the “feel” in your body to execute that touch is gained only through experience and solid practice. See No. 1.
It’s not all purgatory. Many of Shinnecock’s greens are downright friendly with raised edges that funnel shots toward the center of the putting surface. Most however are shaped to repel shots away from the flagstick and in some cases off the green entirely. Be advised: every green features serious undulation. A few are so sloped that it’s impossible to imagine the ball stopping on its own.