What if the ships stopped first at New York or Boston or Philadelphia to offload imports then sailed south to load up with cotton exports? That would limit the time spent in ballast and it the most likely explanation given the comparatively small amount of imports when compared with exports for southern ports.
“No one can successfully run a shipping business if the ships are required to arrive with empty holds, especially when their protected competition does not have to abide by such rules.”
Shall I post the Southern newspaper notices of foreign ships advertising the wares they’ve brought from overseas, or will you ignore those too like the ones posting rates for foreign ships carrying cotton OUTBOUND from Southern ports?
They wouldn't be able to carry a paying cargo while Northern ships would be able to carry a paying cargo. This would put foreign ships at a severe disadvantage in the money making business.
I doubt such an arrangement could be made to work long term with other ships not being constrained in such a war.