I'm going to go out on a limb here and say that this looks like Leptomantispa pulchella, not Dicromantispa sayi based on the descriptions in Cannings and Cannings, the only ones readily available. A perhaps definitive character in their descriptions is that the pterostigma is orange in Leptomantispa pulchella and brown in Dicromantispa sayi. The pterostigma looks orangish to me in Stephen's photo, and even more so in my photo of the same individual here:

Another possible character, visible in photographs here, but not mentioned by Cannings, is that the antennae are all dark (except for one basal segment) in Leptomantispa pulchella, but photos we have here of undoubted Dicromantispa sayi seem to show a few outer segments yellow, in addition to mabye a couple of yellow basal segments. (We may have some images mislabeled as D. sayi--there is a problem!)
The side of the abdomen on our photos from Tennessee, and the images John Oswald identified as Leptomantispa pulchella have prominent thin stripes, not, apparently, present in Dicromantispa sayi. I believe this agrees with Cannings' description.
I hope to hear from the experts, but I'm about as convinced as I can be at my limited level of expertise. As I said, one problem we may have is mislabeling of some of our "Dicromantispa sayi"--they may be Leptomantispa pulchella.

Here's another individual photographed at the station the previous morning--it had also been found on the hood of a car:

Hi Tim, you should post a few of your "action" shots here:

http://bugguide.net/node/view/209650/bgimage

Very sneaky! I didn't know that, like the Mantisfly, I was being photographed.