I got my problem resolved, although I did not particular like the solution. At least I didn't have to do a complete restore. I found the solution in another forum discussion.
With your device plugged into your computer, navigate to the summary page of your device.
- Check the box that is labelled, "convert higher bit rates to..." That's not the exactly wording (I don't have iTunes up right now), but it's something like that.
- On your device, delete the offending greyed out files.
- Disconnect your device from the computer and then reconnect it.
- Once your device shows up in iTunes again, you can successfully drag your music files over to your device.
I dragged about 30 files that previously would not copy and 28 of them indicated they copied over successfully. The other two files had the greyed out circles next to them, but when I looked on my device, I could see (and play) the files actually did successfully copy over to the device. Even though iTunes shows that the files were not fully copied over, they did, so I got what I wanted. Hope this solution helps y'all too.