We investigated low-temperature dynamics in a charge density wave (CDW) conductor NbSe3, a widely studied representative of a class of systems of driven periodic media with quenched disorder and relevant to a wider group of systems exhibiting collective transport behaviors. To date, theoretical efforts have not converged to produce a consistent description of the rich dynamics observed in these systems, especially in the low temperature regime. We developed modern sample preparation techniques and used frequency- and time-domain transport measurements below the second characteristic Peierls CDW transition to investigate the regime of temporally-ordered collective creep in NbSe3 samples in the low temperature regime between 15 K and 32 K. By measuring the frequency of coherent oscillations between two characteristic electric field thresholds, ET and ET*, we show that in nine high-quality samples, pure, Ta-, or Ti-doped, the current-field relation for the collective transport in this regime closely follows a modified Anderson-Kim form across five orders of magnitude with thermally- and field-activated behavior above ET for a range of temperatures. This study, combined with our transport relaxation measurements, provides relevant length, energy, and time scales that set the dynamics in this regime and reveals that the collective dynamics, governed by large length and energy scales, must be reconciled with microscopic local dynamics, with barriers at orders of magnitude smaller scales. The interplay between the collective and local mechanisms set the dynamics that is responsible for extremely slow (creep-like) collective, yet temporally-ordered behavior. Combined with the existing work, our results paint a consistent picture of a transport phase diagram for charge-density waves, and density-wave systems in general, and provide essential ingredients for a much-needed correct theoretical description of these systems.