re: If you had to get up right now and run to the Mississippi River how long would it take?

Per Google, it would take me 4 days and 17 hrs (312 mi) to walk from my house here in Lexington all the way out to the the riverfront walkway in Wickliffe, KY which is right where the Ohio River ties into the Mississippi River.

Of interest to tOT, not much further downriver is Columbus Belmont State Park, where the Confederacy, during its brief stint in charge in Kentucky, ran a chain across the Mississippi River to attempt to block off the Union from advancing further into the South.

IMO, if things had been more fortified at this very point, preventing the Union from penetrating further South under Grant. Once they were able to get around Kentucky and then into Tennessee and on to Nashville, down toward Vicksburg, the writing was on the wall in the Western theater.