I would put the full “little steam” flow rate into the feed line before switching the feed out of the coke drum. This will increase the vapor velocity in the coke drum slightly if continued long enough to get to equilibrium, but the increased steam flow rate will also decrease the molecular weight of the vapor slightly so the probability of increasing the carry over of vacuum resid out of the drum is not as high as you might think. The amount of time between switching the steam in and switching the feed out, at least partially, should be short. If the duration is short enough, the increased steam to the feed does not contribute significantly to increased carry over out of the coke drum as there is insufficient time for the system to come to equilibrium and the increased steam rate may not make it to the top of the coke bed before the hydrocarbon flow rate is decreased by switching feed to the alternate drum.

If you switch steam in early and are concerned about carry over, you should use at least half of the “little steam” flow rate to maintain forward flow into the coke drum as the feed is switched out.