I don't know much about the operations of a shunting yard at a port like Gateway. After locomotives arrive, do they just sit there on the sidings, always connected to the rake of flats, whilst overhead cranes lift off the containers? And the same for when the flats are reloaded? Or do they detach from the train and go off to sit in a headshunt somewhere?
Either way, there is the option of recharging a battery locomotive by plugging it in to a Megawatt-scale charger at the trackside.
The emerging MCAS standard for EV trucks would seem to be an appropriate standard for this. Or whatever 3-phase supply that the Clayton CB45 uses. And because it doesn't need the unbalanced single phase that OHLE uses, the grid supply for recharging batteries will cost much less than that needed to power OHLE.
EDIT: Looking at Felixstowe on Google Earth, I see lots of rakes of container flats but no locomotives. So I assume the locos usually drop off one rake, and then in fairly short order shunt round to pick up another and set off again. So the locos are more or less continuously on the move?