The projection from the basic view direction looks fine to me. Although I do notice in the Spindizzy example, you don't appear to be applying any friction against the ball spinning freely about the world vertical axis, which might be cause the appearance of wobble.

As for rotating the view... you're just rotating the ball around the view Z axis. You need to rotate the projection of the ball around the world vertical axis instead. You can tell this is what is happening by leaving the ball stationary with the number at the top. Rotating the view should leave the number at the top from all four directions, but instead you're rotating the ball as though looking straight down on it (where the view and world vertical axes are parallel).

Right, but your viewing angle is not aligned with world axes. You need to recalculate the ball's "display" rotation based on its "physics" rotation. Assuming in your Spindizzy example that +X is down-right, +Y is up-right, and +Z is straight up, your camera is 60° around X and 45° around Z away from looking straight down (sign will vary based on left- or right-handedness of rotation). That Z rotation should be increased or decreased by 90° each time you rotate the camera.

For minimal change from your current codebase and process... each frame you should make a COPY of your ball's physics rotation, and apply a view rotation to that to match it up to your viewing angle, and then render using that apparent rotation instead of the ball's actual rotation.