The rule that stops this cold for me is: "Note that the distinct numbers being sorted would be hidden. That is, all the nodes in the partial order would look the same."

So, you point to two random nodes and watch them sort? Do you see the "hidden" numbers after they are sorted?

As is, that sounds boring and "random" in the way my sons use that term, without purpose or reason.

If you had more in mind, please describe exactly what the player sees before and after they select two nodes.