At an equal ride height the flat-bottomed oval will ground strike before the circle when you lean it over. The squircle-based body could lean to 45°.
I would expect the formula to provide asymmetry in all three axes, with a 30/70 split in the top and side views. My open-wheel race car design has that, and a lowered equator.
Because it isn't a leaner, it also has a flat truncation on the bottom as you suggest. Every vertex is geometrically defined to as many decimal places as one cares to use.