Silver has it nailed. His point 4B cannot be emphasized enough though he italicized it. You simply cannot shoot line into a strong headwind. (Edit: May be possible with some short shooting heads and very thin shooting line. I don't use them.)
All line has to be shot into the backcast.
An overhead backcast with an off-vertical or sidearm backcast is an excellent cast, and does not have to be a constant-tension or Belgian cast.
Where it really shines (in addition to headwind casting) is in very strong winds coming in nearly perpendicular onto your line-hand shoulder. This perpendicular wind does not affect distance, and you can shoot line both forward and backward.
But, from the moment the fly leaves the water on the backcast, the wind is blowing the line off course, causing a belly to be formed and causing a change in its tracking by the time it straightens out behind you. In order to compensate for this tracking "error" caused by high winds (not you in this case
), you can drift the rod, starting immediately after the backcast stroke, to an off-vertical position.
This will put the "slack" blown into the rod leg of the fly line on the backcast (which will be a long gentle bow) more into the plane of the next forward cast (which will be executed off-vertical obvously. )
The advantage here is that the fly line legs will remain more parallel (but not vertical) on the forward cast, and result in better accuracy and complete fly turnover than with a straight overhead cast.
The above is the exception to the rule that overhead casting is more accurate than off-shoulder.