Recongnizing that the equation should conver different cases without changing the equation is a good point: this also applies to looking at the vehicle moving a snails speed aroung zero. The correct equation incudes this case.
The slow speed case does not directly apply to the vehicle going faster that the wind. However it clearly shows the the equation proposed by electrodacus is flawed and leads to obvious problems there. Looking at this point may also help him correcting his understanding of force and power. Doing the calculations only with power can be tricky if there are processes with less than 100% efficiency (e.g. like the sail).
The equation I use perfectly matches reality. For some reason you think that is not the case but it can fairly easily be proven.
If your vehicle has no mechanical brakes and you want to keep the vehicle from moving in 10m/s wind with a 1m^2 sail then you will need to apply 600W to that motor (all ideal case so ideal motor and no friction losses).
If you apply no power to the motor the vehicle will accelerate towards wind speed.
If you want to go directly upwind with 0.001m/s then you need to supply the motor with 0.5 * 1.2 *1 *(10 + 0.001)^3 = 600.18W
If you want to go directly downwind with 0.001m/s then you can use the motor as a generator and take out 0.5 * 1.2 *1 *(10 - 0.001)^3 = 599.82W (you can just waste this as heat and you can maintain that low speed).
Having an equation with (w-v) or (v-w) is not such a big difference, it is just the sign and this may be different depending on how one defines the direction of force or an axis. One has to look not just at the one line with the formula, but also the explaination fo the symbols.
I don't think Derek's proof has a major mistake in the equations, as it leads to the right conclusion - just getting a result that is not obvious to everybody is no proof that there is an error. Usually math is way more reliable than intuition.
Not sure why you think a change in sign is not a huge difference. It is the difference between being able to accelerate instead of decelerate.
That is the problem the conclusions are totally wrong. The vehicle is not powered by wind directly but by stored energy.