What is the shortcut for changing my primary display?
It's not 100% clear how you're using your screens, but perhaps the following will work for you.

Let's assume your Primary monitor is on the sitting desk. When sitting this is fine, but when you're standing you could just use the Command + Brightness Down Keyboard shortcut to turn display mirroring on so that what's on the sitting screen appears on the standing screen. Then, you can use the same keyboard shortcut to turn display mirroring off when sitting again.