We studied high-density amorphous ices between 0.004 and 1.6 GPa by isobaric in situ volumetry and by subsequent ex situ x-ray diffraction and differential scanning calorimetry at 1 bar. Our observations indicate two processes, namely, relaxation in the amorphous matrix and crystallization, taking place at well-separated time scales. For this reason, we are able to report rate constants of crystallization ${k}_{X}$ and glass-transition temperatures ${T}_{g}$ in an unprecedented pressure range. ${T}_{g}$'s agree within \ifmmode\pm\else\textpm\fi{}3 K with earlier work in the small pressure range where there is overlap. Both ${T}_{g}$ and ${k}_{X}$ show a pressure anomaly between 0.7 and 1.1 GPa, namely, a ${k}_{X}$ minimum and a ${T}_{g}$ maximum. This anomalous pressure dependence suggests a continuous phase transition from high- (HDA) to very-high-density amorphous ice (VHDA) and faster hydrogen bond dynamics in VHDA. We speculate this phenomenology can be rationalized by invoking the crossing of a Widom line between 0.7 and 1.1 GPa emanating from a low-lying HDA-VHDA critical point. Furthermore, we interpret the volumetric relaxation of the amorphous matrix to be accompanied by viscosity change to explain the findings such that the liquid state can be accessed prior to the crystallization temperature ${T}_{X}$ at 0.4 GPa and >0.8 GPa.