Crosses tesselate. I didn't think to take a screenshot, but at least two other people have screenshots showing a 100% efficient layout, with four dice per Yahtzee cup.
1. Maybe this was changed in an update, but there isn't a 3-of-a-kind bonus. There's a 2-of-a-kind bonus, though I don't think boosting the odds of that are worth that many unused dice.
2. I don't think you actually boost the odds at all. I think they're actually lower. With your setup, the dice being rolled only have two dice next to them. Contrast mine (I took a screenshot time).
As you can see, with the exception of the outer edge, every die has three neighboring dice, for roughly 50% greater odds of Two of a Kind triggering. You could have that for all your autorolling dice by adding another 24 dice to your setup, but at that point you have 72 dice to twelve cups, whereas I have half that many dice for nine cups.
I just don't see any way that a setup could be better than this one, mathematically speaking. Every die is being actively used, and has as many neighboring dice as can be crammed next to it while using them all. None of the buffs give bonuses for anything except being next to dice or...rolling more dice, I guess. Aside from rotating the setup 90 degrees, no other setup can match it.