A power transformer vibrating or loudly humming, as in your case, usually indicates something after the transformer is defective and pulling way too much current.
The rectifier tube certainly was the cause of this issue. One way to check this is to simply remove the rectifier tube, if all is well then, you can be pretty sure the issue is with the high voltage supply.
We are glad you found the problem easily.
Best regards,
Frank Van Alstine