build a magnetizer/demagnetizer

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Magnetising ?
Doh ! No wonder it failed. Try to find a design from someone who has something resembling a clue.
You don't need a constant field to make a magnetiser, you need a unidirectional field. So long as it retains the same polarity, a pulsed field is OK.
A solenoid winding (relay, transformer or motor) is a reactive load, which means that it has a higher impedance at AC than at DC. For AC, even at 50Hz, this impedance limits the current. Run it on DC though and it's the same as sticking a fairly short length of copper wire straight across the supply - no wonder it burned out !
Most decent magnetisers are pulsed, using a capacitor bank. Real ones also monitor the winding temperature, or else limit the duty cycle.
-- Smert' spamionam

I built a demagnetizer by making a coil of some (16ga?) magnet wire that I had laying around. Its resistance is way too low to connect to 110 directly, so I connect it in series with a high-wattage device. E.g., a blow dryer. Works fine. Bob