The pistons were all fully recessed. It was so far off center that the rotor was actually all the way up against the metal flange on the caliper on the inside (inside brake pad fully pressed back against the caliper, and rotor pushing on it).
I have some time tomorrow. I'll **** around with it for a few more hours and see if I can figure it out.
If someone would be kind and willing, could they perhaps measure the space between the mounting surface on the R6 calipers and the center where the rotor should be? Mine's 9/8" (no metric tape at home . . . stupid imperial units).
It also looks like someone might have ground down the mount points on this rotor. Is there a popular mod for the R6 that would require that?
Edit: I'm pretty sure someone modified my calipers. The mount point for the lower bolt is 7/16" thick. Will post a picture in a second. Now I have to decide whether extra spacers are okay, or if I need to find new calipers. Pic below: