We study spin S=1 and S=3/2 Heisenberg antiferromagnets on a cubic lattice focusing on spin-solid ground states. Using Schwinger boson formulation for spins, we start in a U(1) spin-liquid phase proximate to Néel phase and explore possible confining paramagnetic phases as we transition away from the spin liquid by the process of monopole condensation. Electromagnetic duality is used to rewrite the theory in terms of monopoles. For spin 1 we find several candidate phases of which the most natural one is a phase with spins organized into parallel Haldane chains. For spin 3/2 we find that the most natural phase has spins organized into parallel ladders. As a by-product, we also write a Landau theory of the ordering in two special classical frustrated XY models on the cubic lattice, one of which is the fully frustrated XY model. In a particular limit our approach maps to a dimer model with 2S dimers coming out of every site, and we find the same spin-solid phases in this regime as well.