> Remarkably there’s really just one way to tie them together

I would rather assume (but knot theorists shall correct me if I'm wrong) that there exist two ways of tying them together:

Cut knots K, L at some point; denote the loose ends by K1, K2, L1, L2.

- Option 1: connect K1 <-> L1, K2 <-> L2

- Option 2: connect K1 <-> L2, K2 <-> L1

Those are the same. To see that, just flip over L before performing the connect sum.