When flying smaller craft I have the impression that the control surfaces move much too quickly. This could be the cause of excessive over-compensation by the SAS. Here is my craft with SAS after a climbing maneuver without any inputs. While I could reduce the Authority Limiter I wish there were a "Dampening" or "Rotation Speed" slider as well . Looking through the Forum I found that this topic has already been  asked in KSP1 and I believe this may be a very similar issue: