Cool concept, but the randomness of the roll is really unforgiving for me. Maybe you can give players the ability to re-roll or put away specific pieces to make it a bit easier to proceed
i just took the idea from Tetris since it's somewhat the closest example.
But rigging the randomness can work too. You can use phantom results to increase chance of specific, less seen numbers to drop in the code, and ensure within a specific number of rolls (9-12), all 6 numbers are presented. Just keep booleans and keep track of the count of each numbers on the board and rig along the lines