I think it would be fruitful to look very closely at the interface between SST(int) and SST(skin).
For definitions see here:
http://ghrsst-pp.metoffice.com/pages/sst_definitions/ It is necessary to get a clear idea as to exactly why the higher temperature of SST(skin) fails to slow down the rate of energy flow from the subskin below.
A. The Default situation
i) Evaporation occurs primarily because of pressure and density differentials between water and air. Thus it will occur even if both water and air are at the same temperature. The process of evaporation is not dependent on any temperature differential. There are other influences that will increase or decrease the rate of evaporation but they need not concern us here.
ii) At Earth’s atmospheric pressure the energy required to provoke evaporation is always less than the energy taken from the local environment when evaporation occurs so we need to analyse exactly where the deficit can be provided from.
iii) In the absence of DLR it is taken from the water below because the water is generally warmer than the air hence the development of a layer of cool water 1mm deep and 0.3C cooler than the ocean bulk below.
B. When DLR is added to the mix.
i) DLR in itself does nothing. Before it can warm anything it must be absorbed by a water molecule.
ii) When DLR impacts the water surface some molecules will evaporate immediately and others will need to wait a moment to acquire enough additional energy.
iii) Those which are in the process of evaporating form SST(int). Those which are busily acquiring energy form SST(skin). The molecules in SST(skin) steadily gain more energy and move upward towards SST(int). In the process they gain more energy and become warmer with sensible energy that registers on our sensors.
C. The response to DLR once evaporation from DLR begins.
i) The molecules in SST(int) evaporate producing a local energy deficit. The energy most readily available is in the nearest molecules of SST(skin) so a flow of energy is set up from SST(skin) to SST(int)
ii) That energy flow is upward so the additional energy being supplied to the molecules in SST(skin) cannot flow downward to increase the temperature of the subskin.
iii) We then have both energy AND individual molecules moving upwards towards SST(int)
iv) The DLR cannot penetrate beyond SST(skin) so ALL the DLR gets absorbed by molecules in that region and ALL those molecules in due course find their way to SS(int). Thus there is no surplus energy from DLR left over to warm the subskin and even if there were it is flowing in the wrong direction.
v) Meanwhile remember that there is a net deficit to deal with when evaporation occurs. If ALL the DLR is now in molecules that are going to move upward and evaporate it can only be provided by a cascade of energy from molecule to molecule up through SST(skin).
vi) But at the bottom of that cascade where SST(skin) has it’s interface with the subskin there is still going to be that deficit. That remaining deficit must be accounted for and it already has been provided by the pre-existing upward flow of energy from the ocean bulk below which is always present even in the absence of DLR
vii) Additionally that energy is already of the correct quantity to make up the deficit because the DLR is ALL accounted for in the process of accelerated evaporation leaving the background equilibrium undisturbed.
Thus DLR in any quantity or from any source cannot alter the equilibrium temperature of the oceans.