I think you've hit on it: washing off the bloom. Our only eggs that fit your description are the ones that for some reason weren't laid in a nest box and got dirty. For example, if an egg gets laid off a roost and spends part of the night sitting in pooh. Or if a chicken has a bit of a poopy butt and dirt gets on the shell. Most of the time a damp cloth will remove any soil, but sometimes the egg then gets the spots you describe. Maybe from the bloom being off the egg. I will wash those eggs and eat them myself.
Do your chickens have a nice clean place to lay their eggs? Are they themselves clean and dry when they go into the nest box? I just chicken sat for some friends who use deep litter in their coop. The eggs were very dirty, because the chickens themselves were walking around in the damp litter so their feathers were dirty.
