We thought of puyo puyo, but we thought it would be harder for unexperimented players to play puyo in an interesting way (the gameplay mostly relying on combos which would be too mentally complicated for most beginning players who would have to juggle with the SHMUP aspect), and, to be honest, we know Tetris to be more visually recognizable and popular.
In a perfect world, the game should be fine-tuned to have a more diverse controls on the screen, and a possibility was to add bonuses and maluses that would alter the game.
Thanks for the answer!