FWIW, a seller of some of these cards on eBay in 2010 offered a group of 16 of them, and they were all New York players (he assumed it was because the radio show was aired only in New York, and he also assumed he had the complete set):

Yankees; Mickey Mantle, Phil Rizzuto, Casey Stengel, Ed Lopat, Frank Crosetti, Gil McDougald RC, Jackie Jensen, John Mize.
Dodgers: Roy Campanella, Pee Wee Reese, Duke Snyder, Don Newcombe, Carl Furillo, Preacher Roe, Gil Hodges, Andy Pafko

The seller said he came across them 20 years earlier (around 1990), and they were all glued to a "matte surface". He said he did some "partial restoration" on them after removing them - so there's a somewhat plausible explanation for the back wrinkles.

I googled the radio show, and it did exist, as it was advertised more than once in Life magazine in late 1952/early 1953. The magazine ad text for the show is virtually identical to the Bowman card backs text.

Again, FWIW. If the printing and fonts aren't appropriate to 1952-53, it's all moot. I wonder if there's any chance, however, that the "New York find" of 16 cards was legitimate, and the non-NY cards seen since then are the fakes?