Salvation has come!
After trying to scrub the sticker with my nails for almost a day, I found this thread and tride Goof Off.
It worked like a charm on my beige cloth visor in 330i. I was able to remove the remnants of both stickers in under 5 min.
tima's procedure is exactly what you need to do. I did not have any bleeding of black paint into the visor material.
I dabbed an old sock wet with Goof Off all over the sticker and then started to brush from the edge towards the rest of the label. It peeled nicely with no sticky residue left behind. Wow!