If I was based in Mobile, and a hurricane was within three days of landfall anywhere along that stretch of the Gulf coast, I would absolutely head inland up the Tenn-Tom rather than waste time guessing whether to run east or west. Trying to outfox a tropical system in the Gulf or Mexico is a fool's errand, as Hurricane Michael proved in 2018.
As to whether going north via the Tenn-Tom is a pleasure cruise, others will have to comment. But, any port in a storm.
"Less judgment than wit is more sail than ballast. Yet it must be confessed that wit give an edge to sense, and recommends it extremely." ~ William Penn