Unfortunately, Kd is also dependent the proportional gain. LabVIEW uses Kp, Ti, and Td.
However, this does not mean you need to throw PID rules of thumb out the window. Generally, I find an oscillating Kp like you did, add Td until I achieve a step response that fully dampens after 1-2 small overshoots (or less depending on the application), and then add in Ti if necessary to reduce steady-state error.
Hope this helps
