no idea here, but i am interested to see if someone knows.

a few things and finally went to Envelope > Make with Warp.

In the warp menu I chose Squeeze and played around with the settings.

Text stayed readable and afterwards I could manualy change the position of the envelope to make it fit.

It will take some time and adjusting but normally it should work

Good luck

You wouldn't happen to have a copy of Freehand lying around? There's a skew setting for Text on a Path in FH that would probably make your life easier.

Idea: Split the text into several sections and use different tools for the jobs. The text on the almost horizontal tape can be easily skewed with warp, distort, envelope or manually. The text that is to disappear underneath the fold/curve is somewhat trickier, and to look realistic would not be all that readable. I would outline the text (keeping an editable layer copy) and manually skew, transform, reflect it under the tape, then either adjust arrangement or create a mask.

There might be other ways out there, interesting problem though. Wanna post a .ai/eps file?

Illustrator can skew & flip the type as well.

Here's a tutorial that might lead you in the right direction:
http://www.graphics.com/modules.php?name=Sections&op=viewarticle&artid=372

Now that tutorial is quite "simple" compared to what you're looking to do, but it may at least point you in the right direction.