This $15 controller on Tindie works with those ubiquitous analog clock movements so that you could do something similar with just about any cheap clock: https://www.tindie.com/products/nsayer/crazy-clock/
Though you're limited to pulses that drive the second hand. So you would have to keep track of pulses and hold one back or add an extra now and then. Something like waking up every half second, calculating current ntp time minus last known ntp time and sending pulses to match.
Daylight savings that goes back would be an issue for that hour, best you could do is wait, or send a bunch of pulses to go around as quick as the stepper allows.