But I think where you run into problems is imagining the situation as two kinds of "pulls" as that puts you back into a reductionist metaphysics of causal forces. You have a literal antagonism of one thing against another thing rather than a complementary pair of things, each of which is essential to the other in a way that justifies talk of a resulting unity or synergy. — apokrisis

I stated in the OP that there is a harmony/unity between order and chaos. The relationship between them is mysterious; they are contentious opposites but are also inseparable, like yin and yang.

And does your dice story fly when there is no reason to expect a "pull" in terms of order at all. The point of a die is to design out the possibility of a correlation between outcomes. The goal is to make a "machine" that maximises our uncertainty by creating a symmetry among the alternatives. — apokrisis

The dice story isn't really meant to be taken literally. It is just a thought experiment to make the reader think more deeply about what randomness really is.