Do you need to exclude the powerline field from an entire room or just the bench area?
How much of a pain the external field is depends on your measurement set up, in particular its common mode rejection and sensor type/ or signal source.
Solution: always go for differential measurements. A transformer can convert single eneded to differential for AC measurements. If you can't do that, then galvanically isolate the input stage.
Magnetic fields have little effect on semiconductors, their cross sectional area (loop dimension) is very low for one thing. Wiring/pcb traces will be the issue.
Put your mesurement electronics in a mu-metal or steel box. Electrostatic sheilding is still needed.
One alternative to heavy magnetic shielding is to add indcutors on the room's sides.
You then use a pickup coil or other mains locked 60Hz (50Hz) and generators with gain phase shift adjustment to drive the coils null out the field. Use Amperes law for a flat solenoid.
B=μ0nI at the centre. A solenoid like this does not produce a uniform field but it may be good enough. If a real uniform field is needed, then use a pair of Helmholtz coils.
www.ck12.org/c/physics/lorentz-force/rwa/Creating-a-Uniform-Magnetic-Field/You can add negative feeback. Use a servo loop (analog or digital) to adjust the amplitude and phase to null out the field. The servo negative fb is driven from a field sensor.
A lo-fi power amp is going to be ok as a coil driver though a power transformer may be needed to adapt the coil impedance to the amp's abiltiy to drive very low impedances.
This has been sucessfully appled to AC/DC scope current probes where the measurement relies on nulling the flux in the probe core.
I read this article on a MEG shielding technique (
https://en.wikipedia.org/wiki/Magnetoencephalography) rooms and that has 9allegedly) nulled external fields down to pico Teslas. The AC flux sensor doesnt need to be ultra linear. A hall device may be ok here. Its also possible to take an average from an array of mag sensors.
The powerline field will have a strong be directional component Start out with one big coil or Helmholtz pair on the box roof and see how it goes. Cheap