Based on your CAD mock up, the light pipe you’ve proposed won’t work. If you really want to get into the details of light pipe design, this design guide covers pretty much everything you would want to know. http://www-eng.lbl.gov/~shuman/XENON/REFERENCES&OTHER_MISC/Lightpipe%20design.pdf
If I was attempting to light the entire outside of the translucent part, I’d start with LEDs on both sides of the board, with light pipes to get additional light to the sides and top of the part. I would also want to heavily texture the part to help eliminate hot spotting, but you’ll probably be stuck with that regardless.
This CAD screenshot shows a something I worked on a little similar to what you’re trying to accomplish. The part was molded out of a milky white material that helped with diffusion of the light.
