Burned wires inside the transformer are most often caused by poor connections at the terminal block. The terminal block set screws can become loose or the contacts become corroded - both cases can cause arcing in the terminal block. This arcing generates enough heat to burn the wires inside the transformer. If the breakers (that control the commons are not tripping then the cause is not overloading, it is arcing in the terminal block. You can try cleaning the contacts in the terminal block with a file and re-stripping the wires, but if the PVC in the terminal blocks is already burned then you need to replace the blocks. If the wire insulation has become brittle then you need to replace the wire.