I'd put the transformer, then not necessarily a torroid, with mains input filter, bridge rectifier
and a large cap + a small cap and a bit of series inductance in a separate metal box you can keep nicely
far away (2 to 3 m or more, use shielded cable) from your low noise regulation box. Saves you
all that possibly expensive shielding effort which even so may be insufficient.
If still not satisfied you might try two back-to-back transformers with careful
passive filtering (100 Hz low pass) in between to get rid of high frequency mush
coming from the mains.
A power transformer with a shield between primary and secondary would be preferable,
but these are expensive custom designs* often for medicinal equipment.
And might be salvaged from such..... Good of a one off but not so good if others
want to build your circuit.
Just a few ideas.
*) just ask Pikatron or Haufe in Germany for a quotation
