In this paper, a new family of solar-sail periodic orbits with adequate properties for polar observation of the Earth and moon is developed under the simplified but nonautonomous dynamics of the solar-sail augmented Earth–moon circular restricted three-body problem. The novel orbits, termed “distant-circular orbits,” are found through differential correction and continuation and employ a simple sun-facing steering law for the solar sail. A basic coverage analysis shows that one of the distant-circular orbits is capable of providing continuous coverage of both the Earth’s and lunar north (or south) poles with just a single sailcraft at a minimum elevation angle of 14 deg and an average range of six Earth–moon distances. Moreover, simple transfer trajectories between orbits of the family are found, so that the sailcraft can switch between observing the northern and southern latitudes of the Earth and moon during a single mission. Subsequently, using multiple-shooting differential correction, all results are migrated to a higher-fidelity dynamic framework that considers, among others, the eccentricity of the moon’s orbit. The perturbations cause the periodicity of the orbits to break, turning them into seemingly quasi-periodic orbits, but it is shown that the coverage capabilities are maintained. Finally, an active control strategy is developed to counteract part of the perturbing effects such that, by appropriately steering the sail, the apparent quasi-periodicity of the orbits is enhanced and the deviation from the unperturbed orbits is reduced.