I tried relentlessly to bind it to Print Screen, Scroll Lock, or any other single key. I ended up adding the game to Steam just to take screenshots.
I looked in the config files - strange that you can change GPU performance presets by modifying an XML file, but when it comes to changing hotkeys, you need to apply to work for AMD, work your way up the ladder until you get into the engineering room, establish a relationship with one of them, get your kids to be friends with their kids, swap wives a couple of weekends, and then maybe you'll be able to use the Radeon Overlay to take screenshots with a single key.