Where did "duck, duck, gray duck" come from?

Duck, Duck, Goose is a common children's game but a typical Minnesotan calls the game a slightly different name: Duck, Duck, Gray Duck. I have never talked to anyone outside of Minnesota that knows of this game as Duck, Duck, Gray Duck.

Wikipedia merely notes that it is a Minnesotan variant:

"Duck Duck Gray Duck" is a variant played by children in Minnesota. The core gameplay difference is that the picker taps the heads of the other players while calling out variant colored ducks and then calls "grey duck" in place of "goose".

There are no notes on why the game is named differently or why Minnesota seems to be the only region that uses Gray Duck.

My question is: When did Duck, Duck, Gray Duck diverge from Duck, Duck, Goose and is there a particular reason why it did?

Garrison Keillor doesn't know, and online sources are all rather contradictory (the game is variously said to have originated in Germany, Ireland, Sweden, and the U.S.) and dubious. So the best answer may well be that origin of the Minnesota name is lost to history, and any answers will be speculative.

I noticed, however, that of all the variants played in different countries— le facteur ("the postman"), plumpsack (lit. "the plump sack"), 수건 돌리기 (loosely, "towel whirl")— only the Swedish name is similar to the English: Anka Anka Gås (i.e. duck duck goose). Digging around a bit more, I did find a site which referred to the Swedish game by a different name: Anka Anka Grå Anka, which happens to translate to duck duck grey duck. An alternative, Anka, Anka, Gråttanka, is attested to on Reddit.

Now, this name is vanishingly rare on the Internet compared to Anka Anka Gås (4 vs 27,000 Google.se results). Nevertheless, Minnesota has the largest concentration of ethnic Swedes in the U.S.— its most common surnames to this day are Scandinavian, and I could certainly envision a scenario where a regional or dialectic name of the game was transplanted by immigrants to became the prevalent usage in the new country even as it faded in the old. The Swedish community was fairly isolated until the turn of the 20th century but has been economically quite successful since.

Duck duck grey duck did not diverge from duck duck goose.

Duck Duck Goose came from Duck Duck Grey Duck, but people forgot what the game was actually about and so they decided goose sounded better and was less repetitive.

The game duck duck GREY DUCK is derived from the story of the ugly duckling. The story goes that all the other ducklings made fun of the ugly one because he ways GREY not the pretty yellow color they all were. As the ducks grow older though it turns out that the ugly grey duck is actually a beautiful swan and turns out to be even more amazing than the other boring old ducks.

There is no Goose or Geese of any kind in the story, therefore it makes no sense to have it be part of the game, either. In the game, the kids walk around the circle and pick out one "ugly" or "grey" duck to single out. That child now must run around the circle to catch his tormentor to prove he or she is not an outcast, but in fact superior to all the ducks making fun of him.

Source: I'm from Minnesota and that's the way it was always explained to me.