I've found a simple steel shield works well in conjunction with rotating to find the least hum. I mount the transformer, get the circuit working, then rotate it for least hum (and that's usually pretty low). Then I mark it, remove it, add a C-shape shield over the transformer, and bolt it down again. No more hum. My mic power supplies (which have an audio transformer in them) have two sections separated by a simple steel shield - for the same reason. I've also only noticed hum problems on mic preamps and power supplies. Even using steel as a shield, I find hiss comes up before any hum does after the shield, with no shield, the hum comes up about 3 to 6 dB more than the hiss.
I've also found another source of hum is coupling in the phantom power feed when I forget that RC filter (220R, 220uF) by each channel. It didn't show up on transformer coupled or dynamic mics but it did on transformerless ones.
-Dale