Both of these alleged issues are bogus.
First, the Morrill Tariff only passed at all after Confederate state delegations walked out of Congress, and so it had very little opposition.
Second, by the time Morrill passed, Congress was thinking about a potential need to pay for military expenses, should Civil War break out -- so the Morrill rates as passed were significantly higher than they would have been, had Confederate state lawmakers been their to negotiate the deal.
Third, the overall 1860 Tariff rates were still 15%, not only the same as in 1792 under President Washington, but also about the same as the Confederacy set for their own imports.
So, in normal times, with full Deep South participation, the Morrill Tariff, if it passed Congress at all, would have represented a modest increase, consistent with past historical limits.
But after the Deep South walked out of Congress, then threatened war, started war and declared war on the United States (May 6, 1861), then Congress found every way it could to help pay the expenses.
As for the question of who controls the Mississippi, we might note that President Jefferson had his former Vice President, Aaron Burr, arrested and tried for suspicion of treason when it appeared that Burr intended to take over New Orleans and declare it his own independent country.
A few years later, Col. Jackson met the mighty British there, just as the song says...
Point is: there is definite historical sensitivity to the question of who controls New Orleans.
However, there's no evidence that Lincoln had New Orleans more, or less, on his mind than any other Southern location before the war.