The Catcher Was a Spy by Nicholas Dawidoff (the book that the documentary film was based on) cites a number of relativs, only one I could definitely find on Geni (Irwin Berg, a NYC attorney who had attended Harvard).
As an fyi, the others are:
(1) a cousin Elizabeth Shames who had a sister
(2) a 1st cousin once removed Ted Berg -- I know there are two int he tree, but do not know where they are from. the one in the book lived in Elyria, OH
(3) Greenbergs, Ginsbergs (Allen was distantly related) and Reichs
(4) Irwin's cousin David. Found a David in the gree, but don't know if this is the same one who went with Irwin and Irwin's father to a baseball game in 1939 when Moe played against the Yankees