It's not mounted in a microwave; it's being bridge rectified into a CLCRC
filter for plasma supply. I get 3 kV DC unloaded. I need to have it in
a chassis as otherwise it makes too much stray interference.
I was thinking of mu-metal foil but those are too thin and would probably
saturate and be ineffective. Using a thick shielding on the other hand
means the shielding will be rigid and buzz instead of the chassis, plus
it presents a cooling problem. I've seen transformers where only the
exposed windings are shielded, with the outer part of the core exposed.
Maybe that will provide enough cooling. I belive they fill those with
epoxy for improved thermal exchange. I need to pull 350-400 mA DC and
the chassis has a fan.

Microwave oven transformers operate with parts of the core very nearly
saturated during parts of the cycle, so they spray magnetic fields all
over the place. Any iron in their neighborhood will be bumped around
like a vibrator. Does your unit still have the magnetic shunt between
primary and secondary? Is the primary the same number of turns it
was, originally? Adding more primary turns (lowering the volts per
turn) will help. Wrapping a thick band of copper around the core in
the direction the turns wrap (an eddy current shield) may help contain
the stray fields a bit, also, at the cost of more waste heat and less
efficient heat removal.