On multiple occasions, I've used black shrink-tubing over a too-bright LED to reduce its glow. I make it so that the tubing closes over the top of the LED a bit, essentially making the visible area on the front of the LED much smaller. Experimenting with different sizes of shrink tubing and adjusting the length and position should produce decent results.

I've done this on both my Mk1 and Mk2 player's standby LEDs, works like a charm. For the Mk1 it was very critical because it's now my living-room player mounted right next to the TV. So the standby LED would have been much too bright and distracting without doing this.