graphics - Rotating an image along a Möbius strip?

I am trying to make a GIF which will be a rotating Möbius strip, with some text printed along its (one!) side. I am trying to (obviously) do this in Mathematica.

After some diligent searching and a previous question I asked, I realize it is almost impossible to get text to behave well when it comes to opacity, rotations, etc. So instead I decided to make a rectangular image of the text, and then import it into Mathematica. But I'm getting stuck on putting all the pieces together.

Do I want to use this image as a texture on the Möbius strip (which I'm getting from a ParametricPlot3D)? Or is there some other way to "wrap" this image exactly once around the Möbius strip?

Also, would it be better to use an Animate to rotate the image - keeping the Möbius strip fixed - or is it better to simply rotate the whole thing? (I mean "better" as in "easier to do / better-looking").

I would actually prefer to eventually figure all this out on my own, but maybe some hints as to how I might proceed would be awesome.

EDIT: After Heike's helpful comment, I've come up with the following:

text = Style["Hello!", 200];
ParametricPlot3D[{4 Cos[a] + r Cos[a] Cos[a/2], 
4 Sin[a] + r Sin[a] Cos[a/2], r Sin[a/2]}, {a, 0, 2 Pi},
{r, -(3/2), 3/2}, Boxed -> False, Axes -> False, 
Mesh -> False, PlotStyle -> {Directive[Texture[text]], Opacity[.5]}, 
TextureCoordinateFunction -> ({#4, #5} &)]

This of course doesn't rotate. But perhaps something can be done with ViewVector or this esoteric TextureCoordinateFunction? I don't know, because my Mathematica is having a very hard time drawing this correctly.

Answer

Here's my contribution. I know you asked for hints only, but I couldn't resist

text = Style["This is some text on a Möbius strip", 
   FontFamily -> "Helvetica", FontSize -> 35];
img = ImageData@Image[Rasterize[text, Background -> None, ImageSize -> 1000]];

Manipulate[
 ParametricPlot3D[{4 Cos[a] + r Cos[a] Cos[a/2], 
   4 Sin[a] + r Sin[a] Cos[a/2], r Sin[a/2]}, {a, 0, 

   4 \[Pi]}, {r, -(3/2), 3/2}, Boxed -> False, Axes -> False, 
  Mesh -> False,
  PlotPoints -> {100, 2},
  PlotStyle -> {EdgeForm[], FaceForm[Directive[Texture[img]], None]}, 
  TextureCoordinateFunction -> ({#4 - t, #5} &),
  PerformanceGoal -> "Quality"
  ], {t, 0, 1}]

The trick to getting a transparent background is to use ImageData[Image[Rasterize[pic, Background -> None]]] for the texture.

Note that I'm using FaceForm[Texture[...], None] to plot the text on one side only. By letting a run from 0 to 4 Pi you traverse around the strip twice, once along the front and once along the back (insofar that you can speak of front and back in the case of a Möbius strip).