re: spinning like a bullet?
I was thinking perpendicular to it's orbit around the Sun.
Flat face of the Gyro/asteroid toward the Sun.
Spin it faster on it's approach to the Sun, perhaps the Gyroscopic force would resist the Suns gravity and the Asteroid doesn't get as close to the Sun thus doesn't speed up as much.
Slow it's spin on the back side of the Sun and it moves closer and is slowwed more.