Distinguishing single-q from multi-q magnetism constrains microscopic spin Hamiltonians. Here we determine the ground state of the candidate Kitaev magnet Na₃Co₂SbO₆ through its coupling to the lattice. High-resolution neutron diffraction reveals a spontaneous monoclinic-to-triclinic distortion at the magnetic transition, in contrast to the absence of detectable lattice-symmetry breaking in triple-q Na₂Co₂TeO₆. Together with strain-selective magnetic responses, this identifies single-q order in Na₃Co₂SbO₆ over the proposed symmetry-preserving double-q state. Uniaxial compression along a low-symmetry in-plane direction achieves the domain selection that magnetic-field training could not, revealing the intrinsic field-induced phase boundaries of the dominant domain. These results establish strain as a symmetry-conjugate field for magnetic domains and highlight magnetoelastic coupling as a route to diagnose, manipulate, and potentially tune magnetic states.