I was having a similar issue and have been thinking about it, could possibly blackout sharpie + electrical tape work? The sharpie could be removed via alcohol wipes later.
I tried sharpie, the ink doesn't seem to really cover the led, i'm not sure how to explain it. I used a thin point permanent marker and the only place i could see black was around it, not over. So i'm guessing it need to be more tar-y in consistence, but also non conductive.
I had not thought of liquid paper or whatever its called. I'd be inclined to try it, but i would probably have to let it dry while offline. And electric tape do block a fair bit, it just never seem to want to cover the led fully, so its still a lightshow over here.
Those S1 are a bit obnoxious. The single red, toned, always on red light on the S5 boards are pretty nice in comparison.