Perhaps adding more concentric shafts would improve any flickering issues when displaying moving images? What is the refresh rate of the device?
If i might suggest, perhaps add a glass enclosure around it, just to make it a bit safer.

Must be a lot of flickering. And motor will consume a lot of power. This thing will be harmful for kids. But it has a bright picture.

How about making a rotating cylinder with leds?

camera frame rate mismatch,power around 100-150w
not for consumer electronics, bright yes ,yes rotating cylinder...

I mean, how about making different shapes of screen? Not flat round picture but cylindrical or conical shape instead.

I can remember an old Soviet sci-fi movie https://en.wikipedia.org/wiki/Teens_in_the_Universe and there was a small spherical device that aliens use to talk to humans. I think such a form will be much safer for in-home use. Interesting about that screen is that it can be viewed from any angle and still displaying the same contents.

I have got a picture: https://pbs.twimg.com/media/Ekovql-XEAAsrCS.jpg

One more thing: in your case color leds can be hold just on flexible pcb, no aluminum armature needed. When spinning, centrifugal force will hold flexible pcbs stright. When spindle is powered off, the whole thing becomes small and easy transportable.