looks like you did use a "low radiation" transformer - a toroid radiates the least mag field - but they have the highest pri-sec parasitic winding C == capacitively couples line noise through the insulation
split bobbin can have 5-10x lower pri-sec C giving them lower line noise coupling to the secondary - but they are the ones that radiate more magnetic field, most benefit from being boxed separately
Agreed, but I still could add an electrostatic shield between primary and secondary since the transformer was made to order and even though stray magnetic field is low it could be even lower using a mu-metal gasket (annealed ).
Any kind of transformer other than that of EI's and toroidals is not available from any transformer manufacturer here in Greece.
I suppose the best option would be to add shielding between the windings but I was kind of reluctant ordering them that way. I might try it next time.