I have three suggestions for match types:
"Single Pick": all three players on a team have to do the same row/column/diagonal. This adds more strategy, as teams would have to pick easy so new players could get a good time, or fast, to win the bingo overall.
"Pool": everyone individually picks a row, and then you basically pick an option at random. You can end up with your own option, a teammate's option, or an opponent's option. The best part is that there can be multiple of the same row/column. One problem with this is that it would be hard to get it set up so that everyone still has 3.5 minutes to route, but what could happen is people see the card in advance, pick, and then find their row/column when the race starts. Better for advanced players, but, then again, not every match should be catered to new players.
"Best of 3": the best player, medium player, and lowest-ranked player on each time each agree to do the same row, without seeing the card. These must be three different rows. Example: Team 1 has high-ranked A, medium B, and low C. Team 2 has high-ranked D, medium E, and low F. A and D must do the same row/column, as do BE and CF, but each pair must do a different row.
There are other random ideas I have, but these three seem to fit the best into the idea of this.
Anyways, I'd like to do this if I have time. I'll definitely have a lot of time to do this in the summer depending on when it is (what day/time).