Rather than creating new images, which will not be quite as good quality as the originals, I would like FotoPlayer to either use the original images, or for me to replace the images produced by JAlbum or FotoPlayer with the originals. My originals are already the desired size and have my name on them, so no more processing is needed.
What would be the best way to use only my original images in albums?
No, in fact that would louse things up. Just choose that option, and make sure that under Album > Settings > Pages > Advanced, the "Copy originals" box is checked. jAlbum will automatically include your original images in the completed album - you don't need to create any special folders.