When it comes to taming the solver, there is a clip from Futurama I think illustrates this well. 
https://user-images.githubusercontent.com/2152766/165919140-2cd352b1-03d1-4919-b332-3149203f3150.mp4
In this case, the car is our solver, Stiffness is the AC whereas Damping is the Heater. They are in direct contradiction to each other.
A high Pose Stiffness means:
I want you to reach this exact angle, fast
Whereas a high Pose Damping means.
I want you to avoid moving fast
Another way to phrase it is that Stiffness relates to reaching a position or orientation, whereas Damping relates to the velocity (speed) in which it gets there. The faster something moves, the greater of an effect Damping will have. It is the amount of opposite force you should apply to any motion.
A Pose Damping = 10 is very high, probably much too high. It likely means there is Stiffness somewhere with too high of a value. Damping should generally never need a value beyond 0-1. At least not how it exists today, because Damping is actually a Damping Ratio. Meaning that a value of 1 means it will have as much Damping as there is Stiffness. And there is rarely a reason for there to be more Damping than Stiffness.
All of this said, there are more reasons for the solver to struggle. An example is really the only way to illustrate what you are seeing, otherwise these recommendations may not work or may even be counterproductive.