Jeanneau Sunfast 36 - Directional instability

when (over?) loading any modern sailboat course stability inevitably has to suffer: the hulls having very much more volume in the back than front, with the (over?) loading the CG will move backwards & thereby aggravate any yawing. Putting more load in the front will not help either, as this will move CLR forward (the comparatively fine bow is immersed further), again aggravating yawing.
Before doing any serious grafting under water, that will require extensive remedial surgery if unseccessful I would try something exterior:
transom mounted casettes with dagger foils, either fixed("stern-daggerboards") or as twin additional rudders. Can be deployed or retracted while sailing & easily taken off from their pintles

 

I have not sailed on a SF36, but I owned a 32 for many years, it was a delighful little boat but somewhat unstable, you could not let the helm alone for even a moment. These were racing boats in their time, we should remember this. Briand is a very good designer and knows how to draw fast boats. Some friends who sailed the 36 say that the helm was very stiff in heavy winds. Originally the boat was designed and built with a tiller, perhaps the problem with your boat is in the excessive (or insufficient) gearing of the wheel. In any case, I would not try to modify a 30-year good old boat. If this boat doesn't suit you, perhaps the best option is to trade her for another one.

 

Boats designed to maneuver fast in a race are not going to track like a full keel heavy boat that has a hard time tacking.

 

And remember, sooner or later you will want to sell this boat. Extensive modifications can dramatically affect resale price.