In my opinion the best way to create a strong enough magnetic field that is powerful enough to clear the tapes is with a powerful magnet.
Not trying to create one by running a ballast.
Powerfull magnet does erase the recorded signal, but leaves the tape magnetized. And because the tape is a grainy thing, when magnetized the grains irregularities cause the field to become irregular along them, hence the noise.
If you want to eliminate tge noise, you need to demagnetize it completely and for that you need a slowly decaying AC field.
The erase head does that to some extend (to the depth of normal recording), provided it is a proper AC erase/bias system (usually operating at few 10's kHz) and not the cheepeese permanent magnet and DC bias recorder.
But it does not demagnetize all the material in the full depth, so the noise from the deeper layers remains, once it was magnetized (e.g. by the typical "whole cassette" permanent magnet eraser; those are intended to destroy the recordings, not that much to clean the tape for new use).