I realize I'm necrobumping this, but it's the first google hit for "regulator circuit valvecaster."
IME, a regulator is unnecessary. Simply using a 36 Ohm, 2 W resistor to drop the 18 V input to 12.6V for the heater circuit is adequate. It's simpler, it doesn't generate more heat than the circuit can handle, and it's plenty quiet.
Another option, if you're interested in increasing headroom, is to use a 12V adapter, run the power directly to the heaters, and use a voltage doubler to supply 24 V to the plate.