First of all, I want to compliment you on your wood and metal working skills. They are an order of magnitude better than mine.
To your transformer "chirping": Having worked fin a company that manufactured them, I can tell you that the source of the noise is the air gap between the pair of core pieces.
Fully encapsulating the transformer in two-part epoxy will eliminate the chirping.
Unfortunately, you would have to remove the transformer from the board to do that.