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.
One of the things that separates Tour players from the rest of us is that the former are intimately familiar with their games. They know how different shots will unfold regardless of where the ball is sitting especially around the green (where difficult lies abound). Not surprisingly that’s where weekend players tend to cough up strokes.
That’s the saw’s primary advantage. It automatically removes any temptation to rotate the putterface through impact and almost assures a square strike. Granted the saw grip won’t work for everyone (remember we’re all different).