We had pretty much the same thing. All three fledged and wobbled their ways off to robin-hood. (Har har har.) But during the whole process, I wrestled with the same worries.
I finally decided that if one fell out and survived, my picking it up and putting it back in the best would probably cause it to be rejected and (ironically) kicked back out of the nest, so I decided to go into ostrich mode, and it all worked out.
I’m terribly tender-hearted, and this wasn’t easy, but taking the long view, the survival of the species, even American robins, means letting nature take its course. *wrings hands*
I’m hoping that more dispassionate posters will have more useful guidance.