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Reddit mentions of Analytical Mechanics of Space Systems (Aiaa Education)
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I looks like the default controller built into the SAS is underdamped, causing severe overshoot. Control gain tuning would help stabilize your specific ship, but the controller would not perform well once you staged.
Personally, I prefer using a Lyapunov-stable control law:
u = -Ks - P(w-wr) + I(wr_dot - w x wr) + w x Iw
s: modified Rodrigues parameters for attitude representation, with shadow set switching
w: body angular velocity
wr: reference angular velocity (zero for reorientation maneuvers)
wr_dot: reference angular acceleration (again, zero for reorientation)
I: spacecraft inertia matrix
K: proportional gain
P: derivative gain matrix
We again come to the problem of gain tuning, however. But we can look into Lyapunov Optimal Control. Something like this paper could help.
I suggest Squad take a look at Chapter 8 of this book.