Jim D, The criticism is for the equation not you. Ein=Eout – delta S, where delta S can be positive or negative for thousands of years. If you have 600 years of positive delta S, the ocean giving up heat due to any number of natural events, you would have a long period of negative delta S, recovery. Then if you select a point to use dF=dH/dt +lamba(dT) without considering delta S, you get confusion.
As the oceans approach some conditional equilibrium, delta S would approach 0, for the oceans, delta S for the atmosphere is faster, but not instantaneous, so there would be a lag, before it reached its conditional equilibrium. It is unlikely to both the atmosphere and the oceans would reach the same equilibrium in the same time period, so there would be oscillation. Since there are several thermodynamic layers in both the oceans and atmosphere, there would be more than one oscillation. dF=dH/dT + lamda*dT is only valid if delta S is zero for both the oceans and the atmosphere. So look at dT, since 1880 it is about 0.6C per century. As the temperature increases, water vapor would increase so at some point that rate of increase in T would increase without any CO2 contribution as a forcing, but with some feedback to delta S. Water vapor would likely be the greatest feedback to delta S, but with albedo change, also a feedback to delta S, biological CO2 might be a larger feedback. All that is pretty obvious.
If the paleo data for estimating the past ocean temperature is off by 0.2C the then the estimate of delta S would be off by 0.8Wm-2. We are trying to determine a change in forcing in the oceans of +/-0.5 Wm-2 with an error of +/-0.8Wm-2. or more.
So your use of the formula is fine, the formula itself is incomplete.