Hi.
Is that 500mA altogether for both supplies or 500mA out of each regulator?
I just checked DigiKey to see what they had for power regulators in TO-3 packages. These almost always get installed on beefy heatsinks to dissipate heat due to large power drops, as in your situation. The 5V version (LM340-5.0CT) needs a HUGE heatsink to handle the 3.5 Watts (7V*0.5A), unless you use forced air, as in a fan. They didn't have a 12V version.
So, linear regulators will need space-robbing heatsinks, and possibly a fan, to handle the dissipated power.
So, you either go with a switcher, which can demand extra parts on the output for filtering not shown in any of the schematics displayed here; or, the simplest way, based on your situation, is to go to a power supply closer to 12V, if not 12V itself.
FWIW.
kenjj