Sorry for the late reply. We never found a solution, so we've stuck to simply moving the path points themselves around. It's a shame because the nulls would've automated a very small but frequent task.
There is a solution!
After pasting the Nulls and its associated Shape Layer, the Effects that are applied to the Shape Layer lose their references to the Nulls — you have to manually re-set these references. So, select the Shape Layer and access its Effects Control Panel. Note that each Null has a pulldown menu — they are now incorrectly referencing the Shape Layer. To correct the issue, simply use the pulldown menu to select each effect's appropriate reference — simply ensure they link to their respective names.
Interestingly, the solution works regardless if each effect is linked to their respectively named Null as long as each effect references one Null. This issue also crops up if you were to copy-paste the Nulls, within the same copy.