Both moment of inertia (rotation) and kinetic energy by linear displacement during vertical pumping cycle are mainly due to the mass of air of the balloon. The mass of the envelope is very small compared to the air mass. The inertial mass increases with the volume, so a magnitude more than the “aero lift” which increases with the area. So the “aero lift” ends up being insufficient when the balloon scales up.
Beside this, a neutral (slightly positive) buoyancy for the vertical pumping mode is better. With a huge buoyancy the descent phase would consume too much power. And varying the heating according to the phases is not an option, nor is the use of hydrogen or helium.
So the ascent phase is assured by aerodynamic lift by Magnus effect. And as the huge inertial mass of air can operate in the two directions of translation, up and down, the Magnus effect alone should absorb both change of directions and thermal currents, by taking account of a very low rate of acceleration of the vertical translation of the balloon and its rotation, due to the huge inertial mass of air. The enormous kinetic energy of the rising or falling balloon is an aggravating factor.
Even re-establishing the rotation to obtain positive lift will not be enough if the balloon descends too quickly due to the winding phase combined with a thermal descent.
A 1 km balloon hitting the ground at 10 m/s would generate a small storm in the surrounding area.