Prim torture for rotations

I know there are several experienced prim torturers here - hence asking the question, you'll understand about the rotations part too.

I need a sort of hoop prim - cylinder with hollow, ring or torus doesn't matter - that will be elliptical at the end of the build - easy so far. But ideally I need it to rotate around one of the 'sharper' ends of the ellipse (one of the intersections of the major axis and the conic if you want to be more pedantic).

Is it possible? This is going to be in a physical vehicle btw, so reasonably responsive and low prim solutions most certainly welcomed!

I know in theory rotation and position offset calculations will allow me to do it too, but when I've seen in them use they tend to be a bit jumpy - is there a nice smooth way to do it this way that anyone's come up with?

advance cut a cylinder so that it's 0.98 -> 1.00; give it a topshear of 0.5 on either x or y (or both); rotate around z axis.