Really cool idea. Level 4 in particular shows off the puzzle element. The small amount of hinting for adjacent planes is a really good feature to have, especially for the level with death-on-contact obstacles.
Input:
I would find W jump more intuitive for (WS)AD movement, but that's a personal thing. Similarly for rotation, an alternate keyboard input would be nice - QE if single axis or arrow keys if a second axis is added to the plane in later gameplay.
I didn't notice the viewport cube and its function until I'd finished, and using it would make the game easier at points. A label or demonstration in the first level could help if you wanted that.