Road cut cliff face with orchids at the top

Today, I went to a road cut near Tuxedo, NC to photograph some really dark purple asters that I had seen earlier on my way back from a trip to Asheville, NC. But, I'll have to have the asters identified from an aster "expert" before I post those images to flickr.

However, while I was at the road cut cliff face, I looked up and saw some white flower spikes at the top that looked like orchids to me. The cliff face is vertical and about 50 feet (~15 meters) tall, so there was no way to get to them straight on. About a hundred yards down the road, where the top of the cliff face came closer to the road, I climbed up and walked back through thick woods and briars to the spot where I had seen the orchids. The water running down the cliff face comes from a seep at the top. This is where I got the close-up shots of these beautiful flowers right at the edge of the cliff face.

Problem is, I am having a tough time identifying this species. Initially, I thought it was Spiranthes cernua (Nodding ladies'-tresses orchid) until I got really close and noticed that they were a creamy-white shade. That would lead me to think that they were S. ochroleuca (Yellow Nodding ladies'-tresses orchid), except that there was no distinctive butterscotch-colored stripe on the underside of the flower's lip.

After photographing them and still puzzled, I packed up my camera gear and headed back down, when I spotted a group of three more plants growing just next to the upper cliff face. These plants had huge leaves! This is rather unheard of for S. cernua as well as S. ochroleuca, but not for S. odorata (Fragrant ladies'-tresses orchid). In fact, these particular plants did have a distinctive fragrance. However, S. odorata is a coastal plains orchid in the Carolinas and not supposed to be found in the mountains.

Now I don't know if I saw two or three different species of Spiranthes orchids at the top of that cliff face. Any help that you wish to offer me with the indentification will be much appreciated...