If I recall correctly the Pace ADS200 supplies roughly 30V DC to the heater not 24V.
Not quite. Looking at the schematic, it powers the heater with full-wave rectified*, but unsmoothed voltage from the transformer, so the peak voltage will be around 30V, but the RMS voltage is 24V, the same as the unrectified 24V AC. They then do zero-crossing detection to only switch at 0V.
The same rectified AC then goes through a diode and from that point is smoothed with a capacitor, creating a 30V DC rail which then powers the 7805 to generate the +5V rail for all the control circuits.
*Through a full-bridge MOSFET rectifier, so no diode drop losses!