But the duty cycle is decreased to 50%
Transformers are not rated by current, but by power. (volts x amperes)
So your transformer is actually rated 480 VA (about 480 Watts since you have a mostly resistive load, slightly inductive).
Therefore you should be able to draw 12 Amps at about 24 Vdc (guesstimate with safety factor) from you power supply, provided you have large enough diodes. Just make sure the transformer doesn't get to hot to touch. (50-60 C)
On the other hand, why DC and not AC, you are just heating a wire. Use a lamp dimmer (one suitable for transformers, not all are) in front of the transformer.
Don't bother with capacitors, you won't notice the difference from 120 Hz.
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