What Reel did was definitely the right way to do this. West System has a whole set of guides on repairs, including replacing cores:http://www.westsystem.com/ss/assets/HowTo-Publications/Fiberglass-Boat-Repair-and-Maintenance.pdf
If the transom is leaking badly, that means the inner skin is compromised, and in addition to replacing the core and reglassing the outer skin, to do a proper job repairing this you also need to open up the hull and reglass the inner skin.
Lastly, make sure you follow the instructions in the West System manual for drilling holes and bedding hardware when drilling holes for the rudder. Otherwise, water will eventually make its way back in, and you'll find yourself in the same situation sometime down the road. Properly done, there is no reason why a repair job using wood won't last for the life of the boat.
Like Div said, the wood adds thickness (technically, increases the moment of inertia), without adding much weight. The end result is a laminate much stiffer and stronger than a solid laminate of the same weight, or much lighter than a laminate of the same strength. Whatever you use for the core needs to be strong and light, especially in shear- body filler is neither of these. There's a reason why wood is used as a core material in a lot of sailboats. You could try
Starboard, but my concern (other than the weight) would be that if the starboard area is much stiffer than the surrounding areas, hard points might develop as the transom flexes and cracking could start again.