It doesn't address the major issue but would they accept small stickers or stamp rather than drawings of thunderbolts etc. It would speed things up maybe and be easier for kids who find writing hard.

A complete aside but ds6 has finally got multiplication. 4 weeks before the end of year 2 (first grade in the US). The teacher says they have been doing it for ages but ds6 doesn't count skip counting or repeated addition. I think they may be using some sort of grid to get the answer though. I think my goal for the summer holidays might be the multiplication tables.