Okay, I'm back. It took a little longer than I had thought to get the material written in MS-Word converted to usable HTML.
If you have not yet read the previous post, "The Answer, part 1," please do so first. What follows here makes no sense whatever apart from what I posted a few hours ago.
Which is not to guarantee that it will make sense to you after you've read part 1. It's a necessary condition, but may not be a sufficient one.
Again, thanks for the earlier responses. I wanted to post on this topic, but it wouldn't have meant a whole lot if you hadn't tried to puzzle through it a bit. To be honest, I'm also trying to create a little bit of interest in the overlap of ethnology and religion.
No responses to that somewhat technical question in the short time I gave you. That's fine. I'm going to present one possibility, but there are more, so if you would like to let your imagination run and share a different workable change of circumstances that would allow introducing some order among the four cultures, by all means, please do so.
The fact that we cannot discover the origin of a story or its development just by looking at some versions as they are stated to us does not mean that we are out of options. In this case, as we are creating a hypothetical model that will hopefully simulate reality before we're all done, we can modify the example. In a real life investigation, we can look for further clues in the cultures that surround instances of supposed resemblance. No cultural form exists in isolation.
So, let's return to the question at hand: In which ways would the circumstances need to be different so that we could actually come up with a credible answer? If we give ourselves the freedom to add more imaginary data, can we construct a relatively plausible way to decide which one of the cultures is most likely the original source for the story? We concede that in the present state of the scenario no conclusions are possible. How can we alter that state (without, once again, invoking omniscience, time travel, revelation, magic, miraculous writings, or anything else out of the grasp of a “normal” twenty-first century scholar)? Let's give ourselves some latitude and invent some further facts that might be accessible to an anthropologist or ethnologist.
Here is an idea of mine. Feel free to share yours. A legitimate place to look would be the languages used in each culture, and we could make up enough additional data in this direction that would make a solution possible. (The ghost of Max Müller rides again. Herbert Spencer would be delighted.)

So, what follows is totally ad hoc and is purely intended to illustrate a possible solution, should the facts of reality present themselves in a favorable manner. The original example was ad hoc as well, and we’re merely describing possible methodology. Of course, there are clear counterparts in reality, but looking at languages for which we at least know the names will probably help our understanding more than my trying to find workable examples in Australian dialects.
Let us then suppose (rather unrealistically) that the languages of the four cultures are: German, Lithuanian, Latin, and English, although, just in case someone should think that it makes a difference, the cultures are not necessarily those of Germany, Lithuania, Rome, or England. The people in these hypothetical cultures just happen to speak those languages. I’m also adding just a few further details, which will help us construct a scenario under which it would be possible to find the original source. The four sentences in the languages I have assigned to them are as follows.
As you can see, I've added the word mergaitė to A, B, and D on the hypothesis that it often comes up when the story is told in A and D, and always in B. However, in neither A nor D does the word have any meaning; it is used as a name. On the other hand, it is a genuine word in Lithuanian, and it means "girl" or "little girl." So, the term is entirely at home in that language, whereas it is not in German or English.
So, the most likely reconstruction is that the culture of origin is the Lithuanian-speaking culture B, and that the initial transmission of the story included the Lithuanian word mergaitė, which cultures A and D misinterpreted as a name. The fact that the sentence in B is longer than in A plays no role; it could go the other way as well. Cultures may expand or contract a story. (Goethe expanded the medieval legend of Dr. Faustus; Shakespeare shortened the life of Caesar as recorded in Plutarch’s Lives. Or was that Livy?) Furthermore, the fact that culture D only makes a brief reference to this girl, and then only indirectly in connection with the ancestors, does not by itself prove anything else either. In this case, the linguistic clue would take precedence over how detailed the content is. Finally since a girl named Mergaitė is otherwise unknown to the mythologies of A and D, it is not surprising that her name would frequently not be mentioned, and that the story often just refers to “a girl.” Other than the choice of languages, the outline of this scenario can be found out in the "real world" (--you know, the place where you supposedly go after graduating from college, assuming that's the deserts of Australia or the island of Tierra Fuego).
A big question is why we would even classify culture C’s myth into the same cycle. The idea of an angry seagull rushing into the forest to discover mushrooms seems to be rather distant from a girl heading for the garden to pick berries and flowers. The connection is admittedly rather tenuous.
However, we can give an explanation that both explains the weird scenario of a raging seagull on a mushroom hunt and ties it into the story. Let's assume that the people in culture C also heard the same story, but, in contrast to the folks of A and D, attempted to find some literal equivalent to the sound of mergaitė and came up with mergus iratus. This is not as far-fetched as it may sound; etymologies can take strange turns. This possibility would gain considerably in strength if a) there were some kind of a mushroom-oriented cult in culture C, and b) a seagull of any disposition or temperament had never been mentioned anywhere else in C's body of mythology, except in this story.
This is one possible scenario in which we are inventing a number of facts, which, once in place, would make it possible to identify the culture of origin with some plausibility. An advantage of this construction is that the main reconstruction occurs right on the level of the data, i.e. the languages used, and we wouldn’t have to invent too many external changes. As it turns out, verbal borrowings are often crucial items in establishing such reconstructions.
Thanks, again, for playing along.
It occurs to me that any number of people running across this entry might have no idea why this topic is interesting or significant. The point is this: I'm following the tracks of Wilhelm Schmidt in his defense of original monotheism, and an important aspect of that project is to establish chronological sequences of cultures.