The Mystery Caterpillars emerged from their cocoons over the course of several days, whereupon we finally identified them as Yellow Bear caterpillars who became Virginia Tiger Moths.
Moth 1, with wonderful antenna fringes identifying him as a male:
Moth 2, a female with smaller antenna:
Moth 3, another male:
The underside is diagnostic (ignore the crud on the aquarium glass):
We set each one on the goldenrod plant inside the garden gate, whereupon they charged up in the sun for an hour or so, then flew off about their business. They may eat a few leaves in the garden, but they’re not particularly harmful to anything and entitled to a peaceful life.
I must organize all their pictures into a life history.
The Smell of Molten Projects in the Morning 
Ah, good to know. So many butterflies and moths that are have fairly generic stages/instars making them hard to ID.
The caterpillars came in three different colors, which certainly confused us. Apparently, that’s perfectly normal for these critters: they all turn into the same thing when they grow up.