Returning to the original piece that kicked off this thread (http://homepages.abdn.ac.uk/nph120/meteo/DroneFlight.pdf) version 2 has appeared that does not make the assumptions highlighted in post 22. There is some difference in the power figures from the earlier version but the return to home speed comes out slightly slower than with the assumptions. In round figures it's still about 10 metres per second, in close agreement with DJI's settings. My reading is that sar104's figures seem to be based on a relationship between thrust and power that is true for a hovering drone but not true for a drone in motion.
The question about how the drone knows it's level is interesting since the software processing gyros and accelerometers needs to be given starting positions to work out changes in position and orientation. I don't know the answer but can only assume there is an electronic tiltmeter within, perhaps something like a miniature pendulum with a means of detecting a tilt signal when the drone is inclined very slightly to the suspended 'bob' . Tiltmeters can be made incredibly sensitive. In short, if this is true then gravity determines the level, just as with a spirit level but with different technology.
I've been thinking about this some more, so that's a timely post. It definitely removes the clearly incorrect element of the previous version - the treatment of horizontal and vertical forces as independent scalar quantities. The fundamental difference remaining between the author's method and mine is indeed the calculation of power expended, but not just for the reason that you mention.
I did use the standard relationship (P² ∝ F³), and I think the main problem with that is that the implicit assumption is that the speed of the incident air is small compared to the exhausted air. In other words the relationship is not airspeed independent and so it will become increasingly incorrect as airspeed increases. I've been worrying about that off and on, because I think that implies that my power estimate will be too low at higher speeds.
The author still separates the calculation of power to hover (from rate of change of kinetic energy of the air) and to overcome horizontal drag (the product of force and distance). That seems inelegant - why not simply calculate total rate of change of kinetic energy of the air to achieve the total required thrust and get power directly? I'll try that for comparison.
The obvious question is why do most of the reports of testing still suggest that the optimal airspeed is rather higher than 10 m/s? The assumption that we both made, that lift is negligible, may be part of the answer. DJI's specifications clearly indicate that maximum flight time is not at hover, but at around 7 m/s. One answer here is some careful still-air flight measurements, which I keep meaning to find time to do.
One last question - are you actually the author of this analysis? The discussion would be much simpler if that's the case.