At the ISSS 2013, a novel concept of variable-geometry solar sail was introduced: deployed in the shape of a three-dimensional quasi-rhombic pyramid (QRP), the sail exploited its shape and shift between center of mass and center of pressure to naturally achieve heliostability (stable sun-pointing) throughout the mission. In addition, mechanisms allowed to vary the flare angle of the four booms in opposite pairs, thus allowing to control the area exposed to the sun without the need of slew maneuvers. Using these adjustments in favorable orbital positions, it is possible to build a regular pattern of acceleration to achieve orbit raising or lowering without the need of propulsion system or attitude control. Subsequent more detailed investigations revealed that eclipses, even if lasting only a fraction of the orbit, have a substantial (and negative) impact on the heliostability effect: and even a small residual angular velocity, or disturbance torque, are enough to cause the spacecraft to tumble. In this work, we present a novel and improved concept which allows the sail to preserve its attitude not only with eclipses, but also in presence of disturbance torques such as the gravity gradient. The solution we propose is to add a moderate spin to the solar sail, combined with ring dampers. The gyroscopic stiffness due to the spin guarantees stability during the transient periods of the eclipses, while the heliostability effect, combined with the dampers, cancels any residual unwanted oscillation during the parts of the orbit exposed to the sun, and at the same time guarantees continuous sun-pointing as the apparent direction of the sun rotates throughout the year. Both theoretical and numerical analyses are performed. First, stability bounds on the sail design are calculated, obtaining conditions on the flare angles of the sail, in the different orbital regimes, to test the robustness of the concept. Then, a numerical analysis is performed to validate the study in a simulated scenario where all perturbations are considered, over extended amount of time. The concept targets equatorial orbits above approximately 5,000 km. Results show that an increase of 2,200 km per year for a small device at GEO can be achieved with a CubeSat-sized sail.