Hi,
Everything you say is correct. All you need is a 12V 20A, or greater, buck (step down regulator) in place of the 5A regulator you have.
A horn normally takes massive gulps of current, so you could smooth this current by placing a high value electrolytic capacitor across the horn. Also, you can put a power resistor in series with the horn (and capacitor). Simply increase the value of resistor until the volume from the horn starts to drop. Maybe start with a 4,700uF (25V or greater) capacitor and a 0.47 Ohm resistor.
One of these 12A buck converters may do your job but, if not, two converters is parallel should: **broken link removed**
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