One of the possible reasons that I could not find his record was that, according to the U.S., Social Security Applications and Claims Index, 1936-2007, he had changed his name sometime between April 1941 and September 1945. But the naturalizations index had listed him by his former name.
In my subsequent searches, I found my subject under his new name in the U.S., Department of Veterans Affairs BIRLS Death File, 1850-2010; he had enlisted in the Army in July 1941 and was released in August 1945. And because he had naturalized in 1943, he would have done so then while he was in the military.
If you go to the National Archives at New York City website for information about their naturalization records, you will find listed under the “U.S. District Court for the Southern District of New York” a separate record set called “Overseas Military Petitions - World War II and Korean War.” The Italian Genealogical Group (IGG) website hosts the Index to Overseas Military Petitions for World War II free of charge. However, note that records are still being added to this index, so it is not complete.
Fortunately, I found my person in this index, and he had naturalized under his new name. The index had listed his name, birth year, naturalization year, the record collection (MP WWII), the name of the court, and a completely different record number from the one I had found listed on the original index card!
The IGG website provides a printable form to request by mail a naturalization record from the National Archives in New York as a well as a link to ordering a record using a credit card. The record fee is $10.00 per copy; $25.00 for a certified copy.