As you have discovered, the traditional canoe shape is far from ideally suited for an outboard.
Cutting it off and adding a transom will get the kicker back on the center line, which is a good thing. A small outboard, mounted as you have it, can result in an unintended bath with a split-second's inattention. DAMHIKT
I assume that the stern of your canoe is squatting unacceptably under power and causing your problem. If so, the solution is to move the weight in the canoe forward to get more of the hull in the water. This could be a tiller extension and moving yourself forward, or a passenger seated well forward, or cargo well forward.
I would not expect a leeboard to help with steering.
Wayne