overpitched,
This thing about reference frames has you boggled, but let me try this:
In this case, there is no absolute energy or momentum. It is all relative to the reference frame you chose. Since you calculate the energy/momentum in one frame, you get confused and wonder where the extra energy/momentum came from when downwind vs upwind. You forget that the wind is a big contributer to the energy/momentum of the situation, perhaps because the air is so clear it seems to not be there.
If you are in a balloon drifting in a 50 knot wind, and you bump into a traffic sign, the energy/momentum is enormous, and you might be killed. If you bump into another balloon, the energy/momentum is small, and you say "Pardon me!". Why? Because these quantities are relative, not absolute, and are dependant on the reference frame you decide to use.
You have decided to stay in the earth reference frame, and calculate all energy/momentum that way. That is fine, just don't mix the numbers to suit your theory (which is that a turn downwind must cause a big performance problem). Where you get an F in physics is that you ignore the enormous energy pouring through your system from the wind.
If we take a 100 foot square of surface, and pour a 30 knot wind through it, we have a constant energy source of about 90 Horsepower, enough to entirely power a small airplane. But you simply ignore this energy/momentum contribution, and have done so for about 10 of your posts! Where does the aircraft get the ""extra" energy/momentum as it turns downwind? From the Wind!