I just got a Stasdock (because purdy)

I just bought a Stasdock rack (installation manual here) I'm trying to install on my office wall. Ir's a 12"x12" frame, with mount points at all four corners. The studs on my wall are 16" apart. I considered bolting a piece of plywood across the studs and attaching the rack to that, but that would look terrible (and looks are kind of the whole reason for the Stasdock). Any suggestions? I'm not sure drywall anchors would hold up, and I don't want to risk my favorite and second most expensive possession to "I'm not sure."