Glassy metallic alloys are richly tunable model systems for surface glassy dynamics. Here we study the correlation between atomic mobility, and the hopping rate of surface regions (clusters) that rearrange collectively on a minute to hour time scale. Increasing the proportion of low-mobility copper atoms in La-Ni-Al-Cu alloys reduces the cluster hopping rate, thus establishing a microscopic connection between atomic mobility and dynamics of collective rearrangements at a glass surface made from freshly exposed bulk glass. One composition, La60Ni15Al15Cu10, has a surface resistant to re-crystallization after three heating cycles. When thermally cycled, surface clusters grow in size from about 5 glass-forming units to about 8 glass-forming units, evidence of surface aging without crystal formation, although its bulk clearly forms larger crystalline domains. Such kinetically stable glass surfaces may be of use in applications where glassy coatings stable against heating are needed.