Looks to me like everyone but Fuzzy Bear was clueless.
It's a difficult question, that's for sure. I think it's possible that much of Louisiana's shift to Eisenhower can be explained by the increasing influence of its (at that time) increasingly Republican suburbanites. As you know, the Republicans first converted urban and suburban areas in Southern states, before branching out into the rurals. Eisenhower won Texas in 1952/56 largely because of his strength in Dallas, Houston, Austin, and San Antonio; Virginia thanks to the Richmond, Virginia Beach, and Northern Virginia metropolitan areas; and Florida due to Palm Beach, Broward, Miami-Dade, Hillsborough, Pinellas, Orange, Osceola, etc. In Louisiana, Eisenhower's path to victory was similar, as he routed Stevenson in New Orleans and also beat him handily in Baton Rouge, Shreveport, and the New Orleans suburbs.
Moreover, like in the other states of the Deep South, many of Strom Thurmond's Dixiecratic voters from 1948 voted for Eisenhower, which helps to explain why he did so strongly in Lowland South Carolina, the Black Belt of Mississippi, and Montgomery/Jefferson Counties, as well as in Northern Louisiana. Deeply racist parishes like LaSalle, which had overwhelmingly supported Thurmond, supported Eisenhower by a decisive margin, and it has voted Republican in every election since. Another factor is that Eisenhower did very well with the Cajuns, reflecting his overall gains among Catholics nationwide.
So in sum, three separate factors: the support of former Dixiecratic voters, the support of the Cajuns, and the support of Republican-trending suburbanites/urbanites, helps to explain why the state shifted to Eisenhower. It was a perfect storm for the first Republican victory in the Bayou State in eighty years.