I just tried steaming my eggs in a vegetable steamer (the silver kind that collapses) and the egg shells just slipped right off of the egg. Amazing.
I only steamed them for 15 minutes and I didn't have time to put cold water in the pot or rinse them or anything. I just turned off the pot and walked away. They did have the grey around the yolk, but who cares, I've been eating the grey on the yolk for 65 years and nothing has happened. When I am rushed 'beautiful looking food' takes a back seat.
The reason they turn gray is overcooking. You could try cooking them for 12 minutes, but my best guess is the problem was not being put in cold water so they actually kept on cooking.