Well, you can certainly add a fin and even mount the jets to it. To figure out how large it should be you'd have to start by figuring out where your center of gravity is located and do a side view area calculation in something like CAD and then add the fin to the side view to move the center of area to a point behind the CG. Split airbrakes will be an option but if they don't open smoothly and together then it'll get ugly really fast.

On a non aerodynamics point don't forget to study the geometry of your wheels and how they steer. You may find that this is a larger portion of your troubles than the fin issue. Any sort of cyclical flexing in the board and wheel boggies may well start things going awry that are not airflow related.