General tips for PID tuning of super low-friction actuator?
1 - Do you have some general idea of what your transfer function looks like? Or at least a frequency response? Could you perform some kind of step response? You could then try to fit an order-2 model on your step response and then try to tune your controller.

2 - You mention that your system is underdamped. I assume that you have underdamped stable poles (in the left-hand plane) in your process transfer function. Perhaps you could place zeroes near the poles to damp the system.

3 - I never use a PID with a "real derivative" i.e. derivative = x[n] - x[n-1], the derivative is always filtered in order to stabilize the system. Otherwise modeling errors and high-frequency noise will be amplified by the derivative which is something you don't want. Or instead of a PID you could use a PI with a lead controller cascaded.

4 - I recommend that you consult this book http://www.cds.caltech.edu/~murray/books/AM05/pdf/am08-complete_22Feb09.pdf