If you start in a city the "cargo" does not expend a movement point to "load". Just set each unit to "Sleep" and move the ship out. Finish the ships turn in the same tile as the next ship, "wake" up each transported unit, then move the next ship to the third ship's tile. If the next ship does not hold as many units as the previous one, only the top ones will be taken (ie Transport hands over to Galleon: only the top 4 will move on). On the next turn move the ships back to their starting points. Getting a two-way flow is really tricky; sometimes you have to park the ships side-by-side to correctly moderate which units get transferred where. If you have the ships, better to establish two parallel chains instead.
A good chain crosses half the map in one turn, because caravan/freight delivery bonuses are based partly on the distance between the sending city and the receiving city. Also minimized the likelyhood of the destination changing it's "demands", which multiply the bonus significantly.
Some of the older GOTM Results pages had screen shots of long or strange ship chains. Look back into the -Teens. They used to give "special" awards for odd situations...