Paul,
In your diagram #3... is there some advantage to the initial rise in the tip path, or is it just something curious you noticed?
And, I am sure there are more than a few mis-understandings in this thread. I know I was not on track with many of the different personal interpretations.
My thoughts were much along Paul's diagram # 1, where the rod moves in a horizontal rod plane and the loop travels in a vertical plane. If the path the rod tip makes is a J with the rod tip moving upward at the end, the loop will be inverted or "underslung". If the tip moves down at the end, the loop will also be vertical but the fly leg on top as usual.
I think I get what Bernd is saying, but he seems to be talking about both rod and loop being in much the same plane, and usually around 45 degrees?
To add to my personal deviation of perception from reality, I do not believe the J in Paul's tip path has to be introduced by the caster's hand during translation. I believe the final tip path can be influenced by a rotation of the wrist. In fact, I have a little routine that I commonly perform when practicing and I am resting from over-doing a particular task. It is almost a "circle, eights, and straights" kind of thing.
ie...
Make a short backcast with a horizontal rod plane and keep the fly leg above the tip, follow that with a forecast with the fly leg also above/ then make a bc above, but the fc below / then make a bc below and the fc above/ then make the bc below and the fc below... etc...
The thing is to mentally call what you are going to do on each stroke before you do it. I find it to be a nice way to rest while still moving, much like slow pedaling a stationary bike between sets in the weight room... only a lot more fun because there is a flyrod involved.