Let me start by saying that I don't have any of these buttons (yet).... but I've been following the thread for a while.
I have an idea on how to light them that one of you may want to try.
I stole this picture from above and "drew" on it:

This will only work using a 3/4" CP top...
Drill a pair of holes at 90 degrees to each other as shown above. Drill the first hole (the side of the LED) into the "edge" of the button holes. Then drill a smaller hole down through the "bottom" of the CP that intersects the first hole.
You should be able to put the LED "body" into the edge of the cp facing the outside of the barrel. The wires can pass through and out the smaller hole to below the CP. I don't think this will interfere in any way with installing the button.
This way, It will be very near to the top of the barrel. The light also wouldn't be shining "up" as much.
One LED in this fashion might do the trick... but you could do 2 (or even 3) around a button.
Hopefully I explained this well enough for someone to try.
I anxiously await results pics.