Coppercone,
How did you measure the flux, type, orientation, probe, meter, scope?
What was the geometry, and type , orientation, loading of the transformer?
Photos, sketch of setup, flux meter/ probe?
Magnetic flux difficult to measure, position, area and frequency dependent.
In audio preamps, even milligauss of mains frequency flux can generate audible hum.
Even a toroid without a gap has a leakage flux.
Shielded power transformers are used in medical, instrumentation, high voltage
Double and triple shields are in so called super isolation transformers.
So far no one mentioned the production solution in Hifi and instrument mains EI, EE laminated:
shading bands ( copper foil surrounding the entire winding/ bobbin and core) to reduce leakage flux
Most high end and pro audio amps, preamps in 1950s..1970s had such shading bands.
Easy to DIY! NO expensive hi mu foil!
All very old techniques,
Jon