Perhaps the best solution is what the bigger tournaments do... one scorecard per player. No excuses because you turn in your own card.
In my experience at tournaments where everyone has an individual card, they're still kept together as if they were all one card anyway. One guy picks them up after the players meeting, one guy at a time (rotated through the round) holds the cards and keeps score, and one guy ends up walking all the cards back to tourney central to turn them in.
The lone exception to this was the tournament where the whole group was required to turn the cards in together. But in that event, each player held a card and kept score for the whole group on that card. At the end of the round, all of the 3-4 cards had to match before they were all turned in together. Zero math errors at that tournament.