I would start with the cleaning because dead band and damping only hide the problem instead of removing the cause. Even worse, the dirt inside the pots works as an abrasive, causing them wear out prematurely. CH pedals aren't too difficult to service, just take care that you get the thin wires in their slots so that they won't twist or get too tight.
Scaling is somewhat related to both dead band and damping, but it won't fix the raw input jitter. Dead band is made for that, but it should be used only after everything else has been tried, mostly with poor quality or worn out controllers. Damping is like using rubber bands instead of steel wires and syrup instead of gear oil. Both are decreasing accuracy. Scaling on the other hand doesn't affect raw input accuracy at all, it determines the relation between your controller input and the flying surfaces. Some like it linear, some exponential. Some people like the latter set in a curve to let them use large hand/foot movements in the center area for better accuracy. Others may like the idea that a certain amount of movement correlates with the actual movement of the rudder or ailerons.
So, you may want to test whether some dead band would kill the raw input jitter, and if it does, clean the pots and test again without dead band to see if that did the trick.
Ink is probably correct in suggesting that small spiking hardly would cause the message. And FLS has a good suggestion for pinpointing the actual controller you're having most problems with. Hand trembles can get worse in the heat of a fight without you even noticing it. There's techniques and exercises for that, similar to those taught to birth-giving mothers for example. Breath, brother, breath...
