For interest, you may interested in my experiences.
I first encountered the instability when developing active suspension (a few years ago). Briefly, the irreversible actuators were controlled by load feedback with a number of additional "loops", including one that fed back lateral acceleration to reduce the rate of change of load with lateral acceleration. We found it best to the reduce roll angle per gn to zero. Whilst playing, we left the vehicle with engine turning & the system powered up. After a time we were surprised (panicked would be a better term) to see the vehicle oscillating madly. We found that the vehicle would always start oscillating with no obvious input (slowly, but building up the amplitude relentlessly until it ran out of oil). If the vehicle was pushed forward (or backwards) by hand, the oscillation quickly died away. Reducing the lateral acceleration loop gain solved the problem, as did the "production" fix of lowering the loop gains overall when the wheels were not rotating. I liked to call the instability "dutch roll", because it shared many of the characteristics of the
aircraft lateral/directional mode.
The next interesting discovery occurred when we were playing with hub acceleration feedback (really, feedforward). It turns out that if hub acceleration is integrated (to obtain inertial velocity) and used to drive the actuators, the actuator displacements can be made to follow closely the vertical displacement of the hubs. Get it right, & the sprung mass can be stabilized inertially (road inputs will transmit no change in load to the sprung mass). One of the problems with the idea is that the system will not stabilize the hub mode. Anyway, we were playing with the idea on track & discovered that in a turn the hub mode would happily limit cycle with (in our case) the sprung mass remaining largely undisturbed. We concluded (rightly or wrongly) that the tyre itself destabilized the vertical hub mode as it recovered from its deformed state.
Both of those experiences were highly artificial, of course, but they can provide an insight into what might be happening in a passive vehicle. My Touring Car experience occurred when one team introduced linear bearing struts to reduce friction. This allowed them to reduce spring rates & damper strengths, controlling roll angle/gn by increasing bar stiffness. Ultimately, this caused the vehicle to "limit cycle" in a corner on a flat track. The cure (Greg's approach) was to reverse the trend a little (i.e. to increase spring rates, re-optimize dampers, and reduce bar stiffnesses). It worked well. It would be interesting to see if similar changes will work in iRacing.