I've thought of several ways to address the issue:
- change the 5V rail to a switching design
- put bigger resistors and mount the 7805 on a heatsink
- have a switching or linear preregulator that drops 12V to a more manageable 7-9 Volts
The bigger resistor solution would also work but I did not have any 10W resistors at hand and I'm not sure they would fit in the small space between the CD tray and the case.
Since I have a few LM7808 and LM7809 from scrap I decided to go with the third solution. So I would basically bypass both resistors, go through the 7808 to drop 2-7V and use the 7805 to drop the remaining 3V.
I started by removing the "leaking" resistors and dead regulator. See the black stuff left behind by the droppers?
The LM7808 is prepared by soldering some heavy gauge wire and add heat-shrink tubing for insulation.