[Bill S (OP)]

Both processes involve an increase in entropy…..

No. Intentionally moving one sock to as known position results in a new but entirely predictable order, hence no increase in entropy. It is just as improbable as the original order!

….. but that increase is a property of the agent of change, rather than the objects themselves. 

Could we be saying the same thing? 

Changing the arrangement does nothing to the entropy of the socks, but the person making the changes increases global entropy.

[alancalverd]

Spontaneous increases in entropy only occur when a system moves to a lower energy state. Doing work by moving a sock certainly increases the entropy of the universe.

[Bill S (OP)]

We have to ask ourselves: does turning a coin over alter the number of microstates accessible to its constituent particles?  Does being shuffled, or unshuffled, change the microstates of a deck of cards? 

The answer, in both cases, has to be, no.

    OK, I will climb off this particular soap box now, and in so doing, will slightly increase the entropy of the Universe.