I agree with you, to properly compare the radial stiffnes of the wheels we need a pre-defined test set-up. What you propose is OK: 10kg applied with a hook on the rim edge.
Now the question: do we keep the force constant for all wheel diameter or do we keep the bending torque (force x wheel radius) constant? I think the force should be kept constant.
When I now think back to the sideway movement of the wheel, I am not sure that the radial wheel stiffness contributes to it because the traction force is applied in the wheel plane. Either the wheel axle bends, either there is some backlash of the right rear joint as you suggested.
I hope your experiments will clarify things 