How to calculate aileron deflection for achieving similar roll dynamics at thin and dense air?
Your conclusions are correct; however, it is new to me that aircraft control becomes "sluggish" at high altitude. Only when you fly up into the coffin corner will control effectivity suffer since you fly close to stall, but that is very similar to the diminishing control effectiveness when you approach stall at lower altitude.

To express your conclusions in the way it can be found in flight mechanics books:


Roll acceleration does not change with altitude because it is dominated by aileron control power and roll inertia, and
The final roll rate will change inversely with the square root of air density because here the roll damping of the wing comes in which is inversely proportional to airspeed.