So I made the Havarti yesterday. First couple of flips using no pressing and the external surface was something ridged like an Alligator skin so I pressed lightly for 2 hours with the regular flipping.
I guess a combination of the cold water bath (2 hours) and relatively quick brining (3.5 hours in a 20% brine) have made for a rather yellow cheese that has a very different feel to it than the other cheeses I've made to date which have all been brined for 12 hours after being pressed overnight. Slightly more give to it, or "rubbery" for want of a better description.