If you spend some time looking through the FB rebuilds forum you'll see members that added a small keel to their hull. Another annoying trait of the FB is bow steer - you hit a wave just right and the bow digs in and all of a sudden you're going a different direction - like 90-180 degrees different.
Spend some time reading the rebuilds where the members describe what and why they are doing the mods they do. I realize your boat is not an Aquasport (Sheaffer) but some similar, or dissimilar, characteristics (besides being flat) might affect it.