Building a filter to get rid of a small DC voltage (e.g. 1 Volt) is fairly easy and there are schematics proposals on the web. Basically it's a 50 A diode bridge shorted to make a bidirectional diode with 1.4 V threshold and a large capacitor parallel to this, like 10 000 uF/4 V. Yes, you can use a hair drier to test, since it includes a diode for half power mode, so it will take some A of DC current in that mode, resulting in local mains imbalance. Anyway, when the hair drier is on, you may not hear the transformer hum...
But there are bad toroids, too. I remember buying some from ebay that turned out to be completely useless due to hum. Those were huge, though, like 2000 VA. Hum was more or less constant all the time. I tried different measures without success.
Regards, Dieter