I actually created a Cricut design that mirrored the outer ring (a solid "wheel" with 4 holes at 12/3/6/9 o'clock), and cut it out in dark blue vinyl (the darkest I had in my pile of vinyl at home). Blocks 90% of it.  Aahh, the darkness.

I guess it is time to cut out some electrical tape in the shape of a skinny doughnut.A little bit harder than the square piece over my VCR's clock...