Variegated June Beetle
I've now got a confirmed ID on this big bug: Polyphylla comes (Casey, 1917), commonly known as the Variegated June Beetle and native to the Southern Appalachians. This one was found in a backyard near the Blue Ridge Parkway, Western North Carolina.
My cats keep catching these fuzzy-buzzy beetles along with June Bugs in my yard and basement. They're big beetles, slightly bigger than the June Bugs here. This one I'm guessing was around 2.5 centimeters long (a little more than one inch). The antennae can fan out beautifully into several "leaves," but the kitties were trying to catch the beetle while I was trying to catch a picture, so he was probably a bit stressed and kept them all neatly folded up. They will vibrate and buzz when disturbed, which of course only serves to get the kitties even more interested in hunting them.
They remind me of the "Maikäfer" (European cockchafer, Melolontha) but don't look quite the same and live halfway across the world. From the reading I've done the European cockchafer is not known to occur in the Eastern US.