Since these things have lots of LEDs, my first thought was to put a range of different tiny delays on them to induce destructive interference, so that the off parts of one LED's flicker are the on parts of another, to smooth out the overall output.

Actually that's not true, my first thought was "just use a layer of phosphor excited by the LEDs", but fluorescent tubes do that and people used to make the same complaints about flicker, so.

Looks like "flicker index" is a useful(?) search term, anyway.