Thank you, Jerboy. The observation that a faraday cage may not do much for magnetic field interference was good. Only 17? Precocious, at least.
A mag field drops off much faster with distance than an EM field, so just a little extra distance may help a lot.
I keep thinking that a detectable powerline induction from more than inches away may indicate some heavy current in the power ground circuits. The normal circuit current is completely balanced in each cable, or should be. If there is current in the ground legs, it will make a big current loop. This would cause just the effect you are experiencing. If the owner has a competent electrician buddy with a clap-on amp meter, it might be worth checking out. It might show up some other problems,too.
As far as shielding, mu metal is quite expensive and saturates very easily. ( Mu ~ 100k) Transformers are commonly shielded by using a shorted copper band around them. Something practical to try if all else fails: Get a small box of romex building wire. Make a big loop of several turns with it and connect it end to end - all the wires - to make a large shorted loop. Then try various positions with it near the monitor/box. If it doesn't work or isn't practical, you've got the wire to install a ceiling fan some day. 🙂