Instead of the bomb dropping, ominously thumping Space Invaders the aliens are Tetris pieces. On shooting one it drops from the ranks. You can catch it with your tractor beam, turn and position it on the ground. Or just let it fall and it will stick where it lands.
On completing a horizontal row
it disappears and drops down. This is important because your own ship scoots left to right along the topmost row. If you let fallen pieces build up, it raises you higher, nearer the advancing legions. I like the idea of the players ship conforming to the angles and planes of the pieces beneath. It might be possible to climb high up on a tower of pieces and shoot laterally at your foes.
I am not sure if aliens here should be able to shoot or not. I am not sure what happens if descending pieces make contact with unsorted tower of fallen pieces. Recruit them back to their ranks? Destroy them? You just lose? Decisions, decisions.
When you lose by coming into contact with a piece, all remaining pieces converge on your ship, squashing and molding it until it becomes a Tetris piece, which is recruited into the ranks.