Goal - reducing the amount to be brought over by mules, without penalizing legitimate alts, penalizing newbies, or stripping everyone bare.
Suggestion - make characters pay for the privilege of transporting extra goods - payment being LP. Those could either be completely non-refundable, or refunded only for goods never removed from storage.
This could be combined with the storage ark idea, from another thread.
Thus one creates a container, which comes with a basic size. One can increase the size by investing LP, much as with one's claim. One can then fill the container, and close it. It is then saved until the map reset. After the map reset, the container can be summoned to any desired spot - once - and objects can be removed but not replaced. (It is, however, thief-proof on the new map - and even once closed on the old map.) It could either operate like a chest (inventory), or possibly allow carryable objects too; those would be more expensive of course - bringing a chest, with contents, would cost rather more than just bringing the objects.
Having any "free" size is a problem for those worried about mules. So either give nothing for free, or scale it with the character's total LP.
Finally, it could also behave like a claim in that one could make it accessible to self only, or kin - or perhaps also to fellow villagers. (Though I don't see how the fellow-villager status will transfer to a new world, when the village idols do not. Still, it would be nice to allow access to a group of others, smaller than one's whole kin list.)
Finally, to avoid mistakes - it should be possible to increase the size of a "closed" container on the old map, fill the new space, and close it once more. People are sure to have last minute ideas of things they desperately need, and thief-proofing cannot reasonably be combined with the ability to reopen and remove objects. Also, as a convenience measure, it should be possible to see what's in one's closed container.
Note that mules are still possible - and slightly advantageous, if one wants to open containers at different times or in different places. But they are also a PITA, and don't convey a significant value; moreover, getting some particular number of LP is easier on a developed character than on an undeveloped alt.
Also note that being able to choose the container location is important - otherwise mules are still a win, as one can bring them to any desired location before transferring their inventory to the characters who will use it.