By normal control I mean quarter-turn rotations and block width movement, but still normal physics after contact (like Tricky Towers). I kind of like how simple Not Tetris gameplay is but I guess special pieces might be interesting addition, maybe in a special game mode.
The point of course would be that these pieces would potentially allow precise placement, so like you might fill straight section more easily with these pieces. Idk if that would be beneficial to gameplay but that's up to you ☺