Instead of evenly distributing the lights on the inner surface we could distribute them at random. That way at "night" we could turn the LEDs to very low and still have "stars". Then during the day we would turn them up and it would be pretty cool to have thousands and thousands of micro suns.
Yeah lets mess up, the entire light sensitive ecosystems of many creatures, just so that we can have meetings on time. Just wait a second and think c'mon.
Repeat for all 365 days.