The Keen ad on page 39 of the Dec. 2, 1957 Billboard lists "Desire Me" above "For Sentimental Reasons". So "Desire Me" that must have been the intended A side even though Billboard's review lists "For Sentimental Reasons" first and talks of "Desire Me" as the flip.
Thanks for the info on the other "For Sentimental Reasons"; I need to add that the King Cole Trio version which you described was recorded on August 22 1946, hit the charts in November, and reached No. 1 on December 28, 1946, beating out another new record "The Christmas Song", which was No. 3. By 1951, Nat had gone solo and was turning out hits like Mona Lisa and Too Young. It was his first No. 1 record for 6 weeks (according to my spreadsheet), Capitol 304, written by Ivory Deek Watson and William Best like you said.
All copies of this disc, no matter what the writing credit, play the same song. It was simply a mistake on the part of Keen Records. "For Sentimental Reasons" was a song written by Abner Silver, Al Sherman and Edward Heyman in 1936 and was recorded by Tommy Dorsey. But that's not the song that Sam Cooke recorded. In 1945 Pat Best and Deek Watson wrote "(I Love You) For Sentimental Reasons" and it became a hit for Nat "King" Cole in 1951. THAT'S the song that Sam Cooke recorded. First pressings incorrectly list the song as "For Sentimental Reasons" and credit Silver, Heyman and Sherman. Second pressings correctly list the song as "(I Love You) For Sentimental Reasons" and credit Watson and Best as the songwriters.
There are two different A-side labels. One shows the title as "(I Love You) For Sentimental Reasons" with composer credits to Watson, Best. The other, illustrated here, has the title as simply "For Sentimental Reasons" with composer credits to Silver, Heyman, Sherman. Except for the 9- prefix on this one, the mx number is the same. I'm assuming they are the same recording, but it seems probable there was major confusion at the label about which song it actually is. Can somebody clear up for us which song is actually on the disc?