This paper develops an observing strategy for space missions performing all-sky surveys, where a single spacecraft maps the celestial sphere subject to realistic constraints. The strategy is flexible, accommodates targeted observations of specific areas of the sky, and achieves the desired trade-off between survey goals. This paper focuses on missions operating in low Earth orbit with interactive and dynamic thermal and stray-light constraints due to the Sun, Earth, and Moon. The approach is applicable to broader mission classes, such as those that operate in different orbits or that survey the Earth. First, the instrument and spacecraft configuration is optimized to enable visibility of the targeted observations throughout the year. Second, a constraint-based strategy is presented for scheduling the observations throughout the year subject to a simplified subset of the constraints. Third, a heuristic-based scheduling algorithm is developed to assign the all-sky observations over short planning horizons. The constraint-based approach guarantees solution feasibility. The approach is applied to the proposed SPHEREx mission, which includes coverage of the north and south celestial poles, galactic plane, and a uniform coverage all-sky survey that maps the entire celestial sphere twice per year. Visualizations demonstrate how the all-sky survey achieves its redundancy requirements over time.