I'd just discuss my project with several people.
They'd advise me to make a smaller version that fits around a GoPro lens.
Here is the result:

It has exactly the same functions like its bigger brother.
There are 30 LEDs around, with a little space to the lens (to avoid shadows) and it get a smaller jack ;-)

I'm also looking forward, to add a new idea.
It will get an adjustment between "sunny-white" and "pure-white" LEDs