having a rotation around something that is not it’s moment of inertia is PRE-Newtonian Physics??
Since I didn’t type a thesis on this, I’ll explain how you missed it.
GRAVITY will pull on this object unevenly if it is rotating on an axis that is not balanced. Since it’s motion is not balanced, the internal force will cause it’s orbital vector to change in the direction of it’s mass as it spins.
The worse it is, the faster it would come down.
Still thinking flogistan?
Saw that scheme years ago on an inertia drive for flying saucers. We had hopes, especially when the inventor built one, but when he made one big enough to carry its own motor it did little but dig a hole in his living room carpet.