I'm not really an expert, but it looks like your grip might end up being like mine was, and that also hurt my first knuckles. The problem was that instead of having my fingers' pads on the rim, my grip naturally went so that the fingertips of the two middle fingers are on the rim, and actually when tightly squeezed my first knuckles touched the flight plate. That makes the finger orientation so that when the disc is ripping out of the hand, the disc isn't pulling your fingers open, but it's pushing your fingertip toward the first knuckle, and that's not a way the joint likes to move. You can get the same effect when you grab your bent finger and pull on it. It hurts.
I moved to "Climo" fork grip, and I haven't had any finger join pain since.