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There is no missing heat in that scenario. The only heat that needs to be accounted for is the 0.5W/m2 imbalance at TOA because if that number is accurate then the only place it can be going is in the ocean.

A two part question on Energy imbalance .

Can we have a TOA imbalance of -0.5 W/m2? If not why not.

ANSWER we are neither a heat source or a heat sink

Energy in is energy out. In other words we cannot have a TOA imbalance because the TOA is where the energy in equals the energy out.

We can have a warmer atmosphere or ocean without having to violate that principal, but only if the input of energy [Sun] varies due to distance [Summer/Winter locally] North and south hemispheres depending on the elliptical orbit of the sun. Or due to intensity [solar Cycles]
In effect the temperature we have is  balance of  the energy in the ocean, land surface and air. In a mathematical model  where the air and sea remained fixed the amount of heating up, the amount of clouds, would run like a clock  and stay the same from 1 24 hour period to the next apart from the energy input.

In our world of currents and Coriolis forces and winds, erosion volcanoes etc where the heat is varies but if one area becomes hotter SOI, PDO, El Nino etc another becomes colder.

Adding CO2  to the air does not make the total energy in or out change one iota. It does modify where the heat is found and this should be more in the atmosphere [ Gates, Droedge, Mosher etc]. The air should be warmer Gates and when it isn’t for 16 years it is indeed a travesty for your argument and the IPCC.

What it implies is that the earth’s atmosphere is a lot more resistant to intemperate changes  than most people here are prepared to realise.

Over the course of a year the average solar radiation arriving at the top of the Earth’s atmosphere at any point in time is roughly 1366 watts per square metre[3][4] (see solar constant)

The Sun’s rays are attenuated as they pass through the atmosphere, thus reducing the irradiance at the Earth’s surface to approximately 1000 W /m2 for a surface perpendicular to the Sun’s rays at sea level on a clear day.

, the sunbeam hitting the ground at a 30° angle spreads the same amount of light over twice as much area

Ignoring clouds, the daily average irradiance for the Earth is approximately 250 W/m2 (i.e., a daily irradiation of 6 kWh/m2)

The insolation of the sun can also be expressed in Suns, where one Sun equals 1000 W/m2 at the point of arrival, with kWh/m2/day expressed as hours/day

1. Making stuff up here as I go.
R Gates, R Pielke on ocean heat.
No one has said what the average heat of the 700-2000 meter level is but a wild guess would say in the tropics [sea surface temp up to 25 degrees centigrade] and Arctic ocean [sea surface temp 3 degrees C] that the deeper level would be about 3-5 degrees centigrade. I.e not much difference at all at depth.
There are no deep hot ocean currents, only cold ones and colder ones.
If the hot currents ever come to the surface they will cool it not heat it [See D Springer earlier on heat sinks and why you cannot heat a warmer body with a colder body] as they are cooler than the surface air . The second thing is heat conducts both ways so at anyone time the hot surface water is not only heating the air above but heating the water below. Which has a lot more molecules than air for the heat to transfer to hence the heat diffusion will for most purposes be downwards by large orders of magnitude.
That is not to say that the surface water might not heat up to 30 degrees C or more in the tropics but it cannot make the air hotter than the water and the water will almost always be colder [please leave out objections like hot air over land blowing out to sea/ night time etc which are not relevant to this argument ] than the air.

2. Pekka Pirilä TOA can be a term for the level where radiative energy out equals radiative energy in. Whether one pumps CO2 into the air or not does not change the amount of energy in by the sun , nor the energy radiated out which is at an equilibrium.
Yes the air at surface levels can be warmer but not because the CO2 is trapping more heat. If that were the case the earth would get warmer and warmer, The AGW argument of climate sensitivity and you might as well argue a sensitivity of 30 degrees instead of 3 degrees.
The reflective surface of the earth is a strange combination of solid liquid and gas. At some point incident radiation is stopped then emitted back.
It matters not whether it is a solid metal spacecraft a meteor or moon they all radiate the heat back. If an atmosphere with increasing CO2 is hotter than one without Then somewhere else in the system becomes colder. ie if the CO2 radiates more heat back to space then the oceans and land will not heat up as much.
Hence there is no radiative imbalance just a poor understanding on our part of the actual way the energy movements occur

3. Sea levels rising reminds me I left a tap running overnight last year?
Surely not.
If the ocean measurements were reliable, which they are not yet proven to be, then the ocean heat content rising would be true but it would mean CO2 was not the cause as there has been a hiatus. What a conundrum.