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Materials composed of spin-1 antiferromagnetic (AFM) chains are known to adopt complex ground states that are sensitive to the single-ion-anisotropy (SIA) energy ( $D$), and intrachain ( $J_0$) and interchain ( $J_{1,2}^{\prime }$) exchange energy scales. While theoretical and experimental studies have extended this model to include various other energy scales, the effect of the lack of a common SIA axis is not well explored. Here we investigate the magnetic properties of $\mathrm{Ni}\left(\mathrm{pyrimidine}\right){\left({\mathrm{H}}_2\mathrm{O}\right)}_2{\left({\mathrm{NO}}_3\right)}_2$, a chain compound where the tilting of Ni octahedra leads to a twofold alternation of the easy-axis directions along the chain. Muon-spin relaxation measurements indicate a transition to long-range order at $T_{\text{N}}=2.3\mathrm{K}$and the magnetic structure is initially determined to be antiferromagnetic and collinear using elastic neutron diffraction experiments. Inelastic neutron scattering measurements were used to find $J_0=5.107\left(7\right)\mathrm{K}, D=2.79\left(1\right)\mathrm{K},J_1^{\prime }=0.00\left(5\right)\mathrm{K}, J_2^{\prime }=0.18\left(3\right)\mathrm{K}$, and a rhombic anisotropy energy $E=0.19\left(9\right)\mathrm{K}$. Mean-field modeling reveals that the ground state structure hosts spin canting of $\varphi \approx 6.5^{\circ }$, which is not detectable above the noise floor of the elastic neutron diffraction data. Monte Carlo simulation of the powder-averaged magnetization, $M\left(H\right)$, is then used to confirm these Hamiltonian parameters, while single-crystal $M\left(H\right)$simulations provide insight into features observed in the data. Published by the American Physical Society2025