I wondered if covering the surface with a grit of some kind and then coating that with something heavy duty would give it an egg-like texture? You could try different grades of grit or tiny lumps and just spray or paint over it with a glue. I'd try this on a scrap piece of card or something first in case it doesn't work.
Practice with different ideas like this on sheets of card and see what looks closer to the JP eggs. I've even seen a type of effects spray paint that gives a pebble/stone texture on anything treated.