The torsion balance introduces fixed biases, and can be operated only in XY plane. So in theory you're right, in practice it's not possible.

Not canceling earth's magnetic field (an easy thing to do) when measuring microNewtons at high currents is just very poor experimental practice. Unprofessional. Amateur.

You could but that may be a bit complicated to set up, while Helmholtz coils are dead easy to make and install. It's just a frame, copper wires, 3 power supplies, a magnetometer and a PC (even an Arduino could drive it).