Per your original statement:
Since we can safely say that the imports destined for southern consumers dropped to zero,
It is sufficient to demonstrate that they were non-zero.
Some time ago, GOPCapitalist posted a record of interstate smuggling activity during the ACW. I remember it well, as it led to a discussion about what scumbags brokers & bankers were, and how they'd betray any loyalties for a buck. The numbers were actually quite surprising.
What you're overlooking is that those imports were destined for a Northern consumer and that the Northern party paid the tariff. What little was later smuggled south doesn't affect that.