I know longer see any reason to doubt the ID of the common burrower nymphs that we found yesterday. They were Ephemera guttulata, and they will be hatching any day now -- perhaps some already have -- as "Green Drakes," in fly fishing terms. Knopp and Cormier (Mayflies, p 105) point out that "seasonally, the duns are on the water between late May and mid-June." Perfect. Note the dark wing pads on the nymph in the picture.
The critical factor to me is the lack of "dark markings" on the abdominal segments. E. simulans (the "Brown Drake") has them; E. guttulata does not. Note that tergites 7-9 on the nymph in our picture are uniformly grayish brown. Now take a look at the same tergites on the E. simulans nymph pictured in Troutnut.com (http://www.troutnut.com/specimen/91). Totally different. You can also find a photo of an E. guttulata "shuck" on Troutnut.com (http://www.troutnut.com/fullsize/picture-im_extax/79), and the terminal tergites look exactly like those on our nymph.
Beaty ("The Ephemeroptera of North Carolina," p. 44) doesn't have much on E. guttulata (in fact he urges monitors to stick to genus level ID with Ephemera nymphs). Still, what he has supports this conclusion.
E. guttulata -- nymphs up to 20 mm: abdomen generally lacking any color pattern. Collected mostly during spring and summer. Mountains only. Uncommon.
The nymph we found was about 1 inch in length -- i.e. around 20 mm -- and it was indeed in the mountains. The Green Drake is a big mayfly, and I hope we can get some photos of some adults in the near future.
Many thanks to my fellow "amateur entomologist" friend whose research helped us with this ID. She's the one who noted the photos in Troutnut.com.