I ran into this dilemma when my kids were young also. I remember we colored boiled eggs and they sat out on the counter in a bowl for DAYS. And we ate them.. no problem! Ever.
I read the same "rules" as you. Don't leave them out more than 2 hours. So I, too, refrigerated, and ended up with a condensation colored mess. Gross.
Spoiled the whole thing for me.
My kids are older now, so I don't bother with it. But geesh. Makes you wonder whats different now that you can't leave them sitting out. Or maybe we're all just paranoid these days. I don't know.
And for whatever it's worth, I grew up (and still live) in South Coastal GA. For those who don't know, it's a warm, humid climate. Somewhere that you'd think heat might be an issue with eggs left out. But we did it my entire childhood, and I have no doubt my mom's childhood was the same. Nobody every got sick and we all loved eating hard boiled Easter eggs with a little salt.
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ETA:
So your post got me curious (when my kids were small enough to do this, the internet wasn't so full of information/blogs/etc just yet. I just used CDC recommendations.
But just now, I looked it up and found several sources that say that AS LONG AS the egg shell is not cracked, then you are good for probably up to a week unless it's full summer with no A/C (100* F). The boiling sterilizes them, and the shell and internal membrane keep out bacteria for some time after. So this explains how we did it as a kid. Because my dad would not turn on the a/c before July 4. It was a rule. :)
So enjoy.
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Sorry to keep editing. This just brought back a flood of happy Easter memories from childhood. We would all go to gramma's house (all the cousins) and every family brought a dozen decorated Easter eggs. The adults hid them and all the cousins would hunt them. Then we'd sit around in swings on the porch and crack them (sometimes on each other's heads) and eat them with a dash of salt. We'd eat 2 or 3 each... it was wonderful. Such fun and simple times. What wasn't eaten was divided up between the families and taken home. My brothers and I would re-hide the eggs after school (or during spring break) and have more egg hunts with them and eat them as snacks for the rest of the week. (Mom always boiled 2 dozen eggs, not just the dozen we took to gramma's.)
Now, nobody uses real eggs. They're all the plastic candy filled things, and kids find them, crack them open and stuff themselves full of sugar. I think things were much better when we ate whole protein as a snack. ;)