Bond disorder in frustrated pyrochlore antiferromagnets can give rise to fundamentally different quantum ground states depending on the nature of the local magnetic moments. Here, we show that the bond-disordered J_(rm eff)=1/2 pyrochlore antiferromagnet NaCdCo₂F₇ realizes an unconventional spin-glass-like state with continued dynamics, in stark contrast to its isostructural S=1/2 NaCdCu₂F₇ counterpart. High-field magnetization and Co L_(2,3)-edge XAS/XMCD establish spin-orbit-entangled J_(rm eff)=1/2 Co²⁺ moments with a substantial unquenched orbital contribution, consistent with local XY anisotropy seen in the isostructural NaA''Co₂F₇ (A'' = Ca, Sr) analogues. μSR and ²³Na NMR measurements reveal progressive slowing of spin fluctuations below ∼10 K, culminating in a partially frozen state with persistent low-temperature dynamics that deviates from a canonical spin glass. Comparison with the isostructural bond-disordered pyrochlore NaCdCu₂F₇, which realizes a random-singlet state, reveals a fundamentally different response of spin-orbit-entangled Co²⁺ moments to bond disorder. These results identify spin-orbit coupling as a key ingredient governing the fate of bond-disordered frustrated pyrochlore magnets.