You state: “... it is far more likely to find [the universe] with some randomly formed clumps, than in a state where everything is distributed homogeneously."

How does this square with the fact that entropy is maximized when ink becomes uniformly dispersed in water?

Entropy is a slippery concept in physics. But this is only because the basic assumptions underlying mechanics (classical, quantum, relativity) can’t recognize entropy as a fundamental property of state. It describes entropy as a property of perception or ignorance of a system’s actual state.

In Reinventing Time, I offer a different take. Entropy is recognized as a fundamental and well-defined contextual property of a system’s state, as it exists with respect to its actual positive ambient temperature.