Thanks for the added info. I like BelSkorpio's and Unregistered's comments.
Another factor in narrow vs wide boards is the lift wide boards get from air under the board once planing. This decreases the wetted surface and causes the board to ride shallower, all suggesting the need for a larger fin.
That is until you reach the "lift off" point and you become air-born. I have done this on my formula board a few times on an overpowered reach, by turning upwind a bit in an effort to slow down. Big mistake!
Formula 160; iSonic 111; HiFly Move 105; Tiga 263; '85 Mistral Superlight.
Maui Sails TR 11.0; 9.2; 8.4; 7.6; 6.6; Maui Sails Switch 6.0; 5.2; Maui Sails Global 4.5; 4.0.