Some science may be necessary on this.
I would suggest poking the carry capacity of wagons, so that they hold less weight. This will force the caravan to send more physical wagons, thus reducing the time that individual wagons take to get loaded again, in theory.
There is the possibility that this will worsen the problem, if the actual issue is one of sorting which wagon will get what good on closeup time. (Inefficient sort algo, now with MOAR lists to sort!) In that case, INCREASING the size, so that fewer wagons are needed would speed up the sort algo processing, by reducing the complexity of the sort.
Since I don't know what the actual underlying pathology is, I can't really say which way it should be poked. It would take science to find out.
There is also the potential issue of a timing loop controlling rate of packing, such that only X items per clock interval are allowed to be packed, resulting in more time being alloted than is possible before the next caravan arrives. In that case, short of a dfhack lua script to poke the timing value, I don't see a solution. (There are a number of compelling reasons for toady to implement such a timing mechanism; it makes the caravan and trade depot more vulnerable to seasonal invaders, if they take forever to leave the depot, increasing the chances of !FUN!. Again, I don't know if such a feature exists... but it would have made a nice, clever fix for the "pause, wait, unpause-- caravan magically loaded!" Bug.)
Initial science to see if wagon capacity has any influence first, then looking for numerical constant to poke second.