I ended up buying a multi-secondary tapped TX that gives me 12/15/18/24/27V @2A, so I guess I can pick the taps that produce, at the filter caps, closest to the 78xx's output voltage plus 3V (I assume the less difference between the 78xx's in and output voltages = less heat generated?).
The p/s is for a combination alarm/security lighting panel - the idea being if a thief chops through an outdoor cable feeding one of the 24VDC reflective PE switches it won't take out the whole system. The theoretical maximum current draw of all the panel's 24V timers/relays/indicators is 900mA.