Not yet reviewed by Pith; the record is open.

Studies of dense core morphologies and their orientations with respect to gas flows and the local magnetic field have been limited to only a small sample of cores with spectroscopic data. Leveraging the Green Bank Ammonia Survey alongside existing sub-millimeter continuum observations and Planck dust polarization, we produce a cross-matched catalogue of 399 dense cores with estimates of core morphology, size, mass, specific angular momentum, and magnetic field orientation. Of the 399 cores, 329 exhibit 2D $\mathrm{v}_\mathrm{LSR}$ maps that are well fit with a linear gradient, consistent with rotation projected on the sky. We find a best-fit specific angular momentum and core size relationship of $J/M \propto R^{1.82 \pm 0.10}$, suggesting that core velocity gradients originate from a combination of solid body rotation and turbulent motions. Most cores have no preferred orientation between the axis of core elongation, velocity gradient direction, and the ambient magnetic field orientation, favouring a triaxial and weakly magnetized origin. We find, however, strong evidence for a preferred anti-alignment between the core elongation axis and magnetic field for protostellar cores, revealing a change in orientation from starless and prestellar populations that may result from gravitational contraction in a magnetically-regulated (but not dominant) environment. We also find marginal evidence for anti-alignment between the core velocity gradient and magnetic field orientation in the L1228 and L1251 regions of Cepheus, suggesting a preferred orientation with respect to magnetic fields may be more prevalent in regions with locally ordered fields.