Wow! that is very interesting that you saw an instability with the I term that low. For future reference, please build up to any values I give you. I realize that I may have misled you saying that we typically don't see instabilities with I term but it is always a good practice to build up to those values especially in your case with a new configuration. So I saw that you also looked at a lower value of the I term somewhere around 0.07. Did the oscillations go away or subside any?
Here is what I understand about the ILMI parameter. The integrator is allowed to build to the IMAX value if the aircraft is on the ground and not level. This causes the pilot to have to make several inputs on takeoff to keep the aircraft going straight up. A leaky integrator was added to Trad Heli to address this issue users were experiencing with takeoff on uneven terrain. The ILMI parameter was added to keep the leaky integrator from washing out all of the integrator error. So the value of 0 for the ILMI parameter essentially doesn't allow the integrator to build while the aircraft is less than 5 m/s. Once it determines the aircraft is moving then the leaky integrator is turned off. Once it gets below 5 m/s then the leaky integrator is turned on again. The idea is to set the ILMI parameter to some smaller value so that the integrator doesn't grow so large as to cause a huge problem when taking off from uneven terrain. Where at higher speeds the larger value of the integrator may be needed to hold attitude and thus the leaky integrator feature is turned off.
My suggestion is to set ILMI back to 0.2 and then ramp up the I term from 0.02 to the highest value where you don't see the instability. The I term is meant to help hold the aircraft at the desired attitude which is really beneficial when flying in windy conditions.
As for the aircraft twitching when the wind blows, do you see the instability oscillations or just abrupt attitude changes that aren't really oscillatory?