My question is how does John add all that rough timbre to his voice on this track. It’s unique from any other CCR track that I know of. Is he contracting his throat to create this sound? Or a nasal register?
Not sure what you mean, because most of the song's style is not different from many other CCR songs. If you mean the parts with coarse-grained roughness in general, that is intermodulation distortion created by bringing the ventricular folds into vibration along with the vocal folds. If he does it properly, he is merely bringing his ventricular folds closer together and adding some breath pressure. I think this is done by tilting the arythenoid cartillages while largely maintaining the poseture of the vocal folds, the epiglottis and the aryepiglottic fold.
I have found that when I perform this song, my voice begins to sound similar to his when I sing it in a key that is almost higher than I can sing, forcing me to almost be shouting, but not quite, so that the singing is strong and loud, and a little bit strained. I don't think I could sing like that for very long, and I'm not interested in trying too. I think I'd be hoarse at the end of the night if I made it part of my signature sound, as Fogerty has. That said, I enjoy listening to it.