There are millions of square kilometers of below sea level dry land, mostly in desert areas. Reducing the mean temperature of the earth by 2 °C requires increasing cloud cover of stratus clouds by about 3% of the total area of the earth (assuming 80% reflection, typical of stratus), roughly 3.36 million square kilometers. I understand there are issues with how much evaporation would become cloud cover (and that cloud cover varies by type of cloud), nevertheless it seems that increased evaporation would increase cloud cover more or less in proportion to the distribution of clouds and most clouds are stratus, thus providing a cooling effect.
Barring the technical feasibility of what you are proposing, there's a few points to consider which make your proposal problematic.
- Water vapor is a greenhouse gas. If you increase evaporation, you increase GHGs in the atmosphere.
- The albedo of water is very low, so if you increase surface area of water on Earth, you decrease the albedo
- Clouds are temporary, not a long-term solution to Earth's albedo.
- The best natural source of high albedo on Earth is snow/ice, not clouds.
- Unless you are using renewable energy sources, pumping large volumes of water continuously will require fuel usage, which will increase GHGs in the atmosphere.
- In order to address the issue of global temperature increase, we need to stop burning fuel as a globe and start sequestering carbon. Efforts to increase albedo artificially are surely of little value while humans still emit 10 gigatons of CO2e per year.
Clouds form when moist air rises in a convection cell - cloud coverage area is largely controlled by the size of the convection cells, not moisture content.
When temperature differences arise between different patches of the Earth, the air over the warmer part expands, creates low pressure, and pulls in moist air at the bottom as it rises. As the altitude increases the pressure drops and that reduces the temperature. When it gets high and cold enough the water falls out as rain. More moisture means heavier rain, starting at a lower altitude. But the size of the cloud is a function of the convection cell size, which depends on the pattern of temperature differences.
To get more area covered by clouds, you would have to change the balance between warm areas and cold areas, so that the warmth was less intense and more geographically diffuse and the cold bits more intense and more geographically concentrated. The average temperature increasing or decreasing doesn't change the differences. Even the differences getting more or less intense doesn't change the sizes of the patches where it is higher or lower than the average. It's a third-order effect.
Cloud physics is very complicated and not fully understood, and it's effect on the global energy balance likewise. Clouds form in warm areas, in the process cutting off the sunlight and cooling the land beneath them. They act a bit like a thermostat, smoothing out temperature variations - although not in the sense of aiming for a specific temperature. This results in feedback loops with various time delays - local warming causes more clouds causes local cooling causes reduced clouds. Their effect on the global energy balance depends on their altitude. Low clouds are made of warm water and radiate lots of infrared to space, high clouds are cold and radiate much less. They have different effects during the day and the night - at night they cause less infrared to be radiated to space, being at a higher, cooler altitude, causing net warming. So what effect they have depends on what time of day they form. And there are feedback interactions with the temperature of the oceans which cause a massive time lag compared to the land which warms and cools very quickly, the effect of mountains and terrain and vegetation, different amounts of sunlight at different latitudes and seasons, and so on. The effect on the climate of clouds at the equator is very different to the effect of clouds in Antarctica during the long darkness of winter.
Feedback cycles with time delays result in oscillations, and an oscillator forced by regular pushes from an independent driver (like summer/winter) tends to result in the phenomenon of 'chaos', as pioneered by the meteorologist Edward Lorenz. Even with perfectly understood deterministic rules, the behaviour can be irregular, complex, apparently 'random'; a fractal structure with variation on every time scale.
In addition, the effect on global mean temperature is a cumulative process. If one supposed the net cloud cover over a year was a random number, centred on a fixed value but varying slightly from year to year, then the amount of heat in the system would be pushed up and down from the previous year's value by a random amount - a classic 'random walk'. If you plot a sequence of independent random numbers, you get a uniform fuzzy cloud of points. If you plot the cumulative sum of the same numbers, you get a rough line that wanders up and down like a mountain range. Over short periods, you get what appear to be rising and falling 'trends', just from random numbers. It's very hard to distinguish this sort of thing from deterministic drivers; different researchers have come to radically different conclusions based on the same data. When the process driving it is not a nice, independent, mathematically well-behaved random number generator, but a chaotic process that can hop between different meta-stable states at long intervals, the issue is even worse. The natural background level varies by relatively large amounts over long time periods. Clouds add precisely this sort of noise to the climate.
There isn't any global shortage of water surface to evaporate from - two thirds of the Earth's surface is water. And it's not generally any cloudier over the sea. Clouds are driven by temperature differences causing air to rise or fall convectively. Clouds rising cool, and drop the excess moisture as rain. More moisture results in thicker cloud and more rain, but not necessarily a greater area covered. And the effects of cloud on climate are not so simple and straightforward, or easily understood.
If you really want to reduce the albedo of the Earth, you'd be better off painting the ground white. Clouds are a highly unreliable way of doing it.