I think I found it!
Triphora gentianoides
Gentian Noddingcaps
https://www.flickr.com/photos/...
http://plants.usda.gov/java/co...
http://www.efloras.org/florata...
The description seems to fit exactly, from tubers, to color of stems, to flowers facing stems instead of outward, and only opening slightly, to habitat from full sun to shade of pine woods.
Apparently the flowers do open a bit more than I've seen.
http://www.regionalconservatio...
I'll keep a close eye on the ones I have in pots and try to catch them in the act of being in bloom!
Thanks for everyone's input.
