Well guys, I was able to fix all of the backlights! I ended up converting everything to white LEDs since I couldn't find the right voltage incandescent bulbs (turned out to be a 6-volt source instead of 15 volts - I figured this out the hard way when the first bulbs I bought barely glowed when powered...I guess my old analog multi-meter didn't work right. I bought a new digital one which gave the correct voltage).
Anyway, here's the pics!
LEDs installed under the clock to serve as a clock backlight:
On:
LEDs installed in the radio dial bracket:
Put back together:
On!
Clock:
Radio dial:
Turned out pretty good! The clock backlight is dim, but you can clearly see the clock in the dark. The radio dial is a lot brighter than it used to be!