I've ruined six eggs already. Can you help me save the rest?

I’m having troubled peeling my eggs. I usually start peeling them as soon as they cool off but I let them sit this time while I went to pick my daughter up from school. Now the shells are only coming off in tiny pieces or attached to egg white, leaving me with only the yolk. These are not going to be pretty deviled eggs. :(

Is there anything I can do to make the shell come off a little easier or do I need to start over? I would hate to waste anymore eggs.