Thanks for all of the suggestions. Unfortunately, I've tried them all and it still streams from the spinning drive unless I delete the files. I want to use the spinning drive as an internal backup drive, so I don't want to delete those files. As far as I know, there is no way to keep Windows from accessing that drive as long as it's connected to the motherboard. If anyone knows of a way to do that, please let me know.
I still don't understand why it won't use the files on the SSD. Sonar goes to that drive to open the project file, now that I've changed the folder locations, but even though the audio folder is in the project folder on the SSD, it still goes to the spinning drive for the audio files.
As I stated in my original post, it isn't just Sonar that accesses the spinning drive files instead of the SSD files. Windows Media Player does also, so I think it must be a Windows issue, but I don't know of any settings to control that. Can someone enlighten me?