playBunny: I've mentioned the excessive frequency of "near-misses" below (when discussing my 2009 data).  But that could result, as you suggest, solely from the excessive re-appearance
of just 1 of the dice in the responder's roll.  In my 2008 data, the frequency of responder's dice not matching either of the opener's dice was only about 1/2 of expectation.

No doubt that the re-appearance of one of the dice is excessive.  Later today, I'll have a better idea just how excessive it is.  And I will take a look to see whether the "other" die in such cases appears to be completely independent, or also shows signs of unusual influence.

2 other notes regarding the exclusive focus upon the the first 2 rolls of the game:

Psychological:  I think humans tend to notice/remember items that appear near the beginnings or ends of lists or sequences.  It's an effect seen in some memory tasks.  That might have been a factor here.  I think that repeated rolls would more easily get our attention when they occur from the commonly-seen, symmetrical, initial position.  Typically, we don't have much complicated stuff to think about during the opening rolls--maybe trying to remember what's best in a GG situation--so we can afford to think about other stuff...such as the frequencies and patterns of rolled dice.

Practical:  As an investigator, I can be more confident that games will contain at least 2 rolls.  That doesn't always happen, due to timeouts, etc.  But it makes data capture much easier.