Your attempted explanations miss by a country mile for several obvious reasons:
1. The exports in 1860 were still low despite that huge boost in MN production you noted. If 1860 was so great, why was its export so much lower than 1861? In 1861 they shot through the roof rising from 4 million to 31 million bushels for the nation. (1858 and 1859 were 9 and 4 million bushels respectively.)
2. One state doesn't account for it--in this case it would only account for a small fraction of the total anyway.
3. The exports stayed at similar elevated levels (37, 36, 24) until 1865 and 1866 when they returned back toward prewar levels (10 and 6 respectively.) If things are as you believe, this drop should not have happened. Or are you suggesting men returning home from war produce less...and stop using reapers...and suffer from worse transportation?

4. The drop in '64 might even be consistent with reopening of the Mississippi and various territorial gains. And in 1865 the market to the South would be open again as well.