don't destroy the xfmr's bobin, insulation soldering the belly band - may even want a wrap of kapton tape to maintain creepage/clearance distances if it is a pcb pin mount style
mu metal is not needed/useful anywhere near a line power transformer - mu metal saturates easily - only used to case very sensitive components - knock the mag field down by shorting with cheap iron 1st
while a box with more sides is better for shorting the leakage mag field - just a strap bent in a U as much taller than the xfmr as fits should help a lot
1) Kapion tape as a layer between the copper and the trafo to protect it, will it take the heat?
2) Are you suggesting a upside iron U over the trafo?
Sorry my ignorance - but I am a total novice at this stuff :) But if we sort this out, the new Leben mod will be legendaric :D