It seems most people have adopted safe and effective means of dealing with crosswinds. It wasn't too long ago that one could observe fly casters hitting themselves over and over because they would not adapt. I think the internet has had a very positive influence in that respect, meaning that people discuss things and learn what others are doing even in mid-winter in forums like this one.
On topic -
I've been a backward caster for many years, having an eye surgeon for a brother who emails me images of mishaps
I insist on my clients backcasting in crosswinds or will change the route for the day to put them on the strong side.
Actually fishing the backcast does not lessen your ability to reach fish, in fact it strengthens your casting because 50% of a flycast is the backcast and being able to drive this backcast makes the forward cast more potent when you switch back.
The body does not have to turn back to target, just shift your casting shoulder to the front and reach across the body a little. Rotate the body a bit (approx 90 from normal toward the other side of the body) keeping the eyes forward.
The key is the keep your knuckles toward the target, thus making it a back(hand) cast. The traditional cast across the body reverses the hand to push with the thumb. The backhand cast does not.
Another secret is to lean the butt of the rod against the inside of the forearm during the stroke to target. This has the effect of really flexing the rod with power that is frankly hard to find on the strong side.
Regardless of how you deal with a crosswind (left hand, cross body, back hand) it's key to keep the path of acceleration true otherwise all the power you apply dissipates into open loops or off-line vectors.
Wind adds tension to the line in flight thus actually helping the fly cast in most cases.