After many tries, with “real” strips or with paper strips, we have a solution \o/
Near to the equator, the strips will be placed according to the parallels. Near to the poles, where this placement is no longer possible, we will place them in parallel to a meridian (see picture below). To connect these different sections of strips, we will make holes to solder wires, which will be connected together inside the ball.
Near to the poles the LEDs will be in staggered rows. The white strips come from an older project. Ours have an higher density, as you can see on the corner in the second picture. Therefore, you have to imagine that there is another LED on each connector.