"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.
A big problem I see with types that restrict a player to a single row is that it's generally unfitting for a team format from bingo-to-bingo. Across a "season" or whatever you want to call it, results will maybe average out (if you use some kind of scoring system but that seems kinda clumsy to me) but in individual bingos, the high-rank players will finish first with some variation, the mid-rank players will finish after and then just sit there while they wait and see who wins, which is entirely dependent on which team has the better low-rank player.
One of the most discouraging things when I was starting out with bingos was seeing people in the IRC talk about doing a rematch while you still have 40+ minutes left to play, it'd probably be even more discouraging if I was part of a team and had my teammates sitting around doing nothing while waiting for me. This happens a lot already in blackouts.
This is why I'm heavily in favor of types that allow usage of the entire board or at least allow switching of objectives (Maybe each player picks a row and as a team, you can switch objectives a total of 3 times?) or otherwise you're usually going to end up with the high-rank players twiddling their thumbs after each game.
