Well, the results are in - and, other than the fact that both the Dreamer and the Sleeper gem patterns are stretched length-wise and width-wise, there seems to be no hidden logic to it. It's probably not even right to say they were "stretched" because that would imply some uniform displacement or scaling across a certain direction, but that is not the case. Instead, I'll just call it "deformation".
For example, the ratio between constellation and gem diagram of the distances between the two top stars of Sleeper is dramatically different from the ratio between constellation and gem diagram of the distances between the two base stars. Another example, in the Dreamer, a few of the points overlap almost perfectly between the stars and the gems while others are way off. Deformation between the Dreamer and the Sleeper is also inconsistent, especially in the deformation lengthwise where the Sleeper gem pattern has been deformed dramatically more against its constellation versus the Dreamer gem pattern and its constellation.
What it looks like is someone roughly modeled the gem patterns to reflect the stars but with no real precision or scale and no intention for precision or scale. In conclusion, at this point, how close a constellation will resemble its gem diagram is really a crapshoot. And so, the world may NEVER know whether the proposed Dancer formation is the real thing...or maybe we just give it a week or two and find out the other way.
[Here is a quick reference diagram demonstrating how the overall constellations as a whole were deformed versus their gem pattern counterparts.
Notice that the Dreamer formation was deformed more evenly horizontally and vertically than was the Sleeper formation. It's quite inconsistent.]