I read a theory that the crossword maker had unconsciously picked up these words being used by kids, who themselves would like to hang out near soldiers that would use those code words.
That is mentioned in the footnote: “it was often his practice to call in 6th formers and ask them for words for inclusion. At that time the US Forces were liberally strewn through Surrey, particularly in the Epsom area and there is no doubt that boys heard these code words being bandied about and innocently passed them on.”
This sounds absurd to me. Ordinary soldiers are unlikely to have been told the codewords for their area of operations until the last minute. They certainly wouldn't have been told about other code words for other areas of operation that they were not part of!
I don't buy it one bit. I also find it unlikely that the bulk of the invasion force was in Surrey in May '44. I think they might have moved to the coast by then.
The wikipedia article on this topic also indicates that there is some reason to suspect that the crossword author was not being entirely truthful about it, but at the end of the day, who knows.
