Well, that's until now!
Step 1: Parts
LED Illuminated Pushbutton - 30mm Square
Also, I got my RGB LED's from Adafruit. Any 5mm RGB should work, but I strongly suggest you get diffused because otherwise you'll get a pretty evident "hotspot" on the button face.
Diffused RGB 5mm LEDs
Also, and this is pretty important, the wires I used are 26GA, I think much larger and this trick may not work.
Step 2: Wiring up the RGB LED
Second, solder the wires to the leads.
Next, slide the respective shrink tubing up against the LED. The length of these need to be as little as you can get away with. This is because if it's too long, the LED will stand too proud, and may restrict the movement of the button, along with not looking very diffused.
After shrinking the individual leads, slide a large shrink tube against the LED and shrink away (again, make as short as you can get away with).
Step 3: Disassemble Button
Next, get the LED connector assembly (white with brass tabs, pictured), and pop those brass tabs off.
The area where those tabs were are going to make the space for the wires.