The cake pan was wide so that edge effects were minimized. There wasn't much wind anyway. The pan was in intimate thermal contact with the pool surface, which was the important factor. Furthermore, even if the evaporation rate was 25% in error (certainly an overestimate), that small correction would have amounted to a pool level drop of 1.5 +/- .08 mm per day -- a small error. I used pool water in the pan, of course. I don't consider any of that "terribly flawed."
I checked the pool level before the pump went on and after the pump went off (7 hours pump time). I checked to see if the before and after levels had different rates and averaged them over a week. There was no measurable plumbing leakage.
Your scheme of putting a bucket outside the pool looses the integrity of thermal contact and introduces different wind conditions. I consider that flawed. Your suggestion of 3 days was not nearly enough considering the undulating pool level. You make no mention of multiple pool measurements to minimize that error. You simply did not look deeply into the physics of the situation, and have a poor sense of experimental design.
Now, back to your OP. You adamantly stated that you must know the absolute climate temperature (and in my example of the pool, you said, "you first need to know how much water you have"). You did not directly comment on the validity of the water loss equation,
(Drop of water level per day in mm) x (total surface area in sq. mm) = (total loss of water per day in cubic mm).
You seem to implicitly accept it, but you digressed again about a flawed hypothesis. Suppose we have an accurate measurement of pool depth as a function of time. Do you disagree that the above equation is valid?
Finally, linear regression on a data set results in two numbers: the y-intercept and the slope. The word "warming" implies a change independent of absolute value. It could be "warming" after a winter in Siberia or Miami; i.e. warming implies a rate of change, independent of the y-intercept. So you still have not given a reason why the absolute temperature at some point in time (the y-intercept) or the absolute amount of water in a pool is relevant in computing the slope in the global warming data (or water loss in a pool).
