Yes and sleeve all the wires, you're relying on relatively fragile enamel to insulate them. It's alright on the coil, there's only a few volts between adjacent layers and even less on adjacent turns but where the wires go to the switch you will get full mains voltage across what is little more than a coat of paint. Yes it should be OK but any flexing and chafing or bending will damage the enamel and you will get a short.Just gonna whip the tranny out again
Stress the "Be safe with all that....".The next basic test could be putting 240Vac into each end of the primary as co-joined and seeing if the secondary gives the expected stepped down output?
The same testing could then be done on the newly made rectifier. Be safe with all that....