I'd say the expanding foam is the way to go, but rather than do the chicken wire or spraying the foam directly onto the lights, what I did was:
I set down a piece of cardboard, then put various items like cups, a small ball, etc, on the cardboard to create random lumps and bumps, then covered the whole thing in plastic wrap. I sprayed the foam onto that. This way, the stuff underneath wasn't covered in foam, and the plastic wrap will peel right off the foam. Once it was dry I spray-painted it.
It's hollow on the inside so you can then just put your LED lights etc underneath. I put a string of red LEDs and five or six cheap flicker-flame candles under mine and it looks pretty good.