"All I Wanna Do" also really sounds like a Brian thing to me--those high guitar parts throughout, the amazing bass sound, subdued drumming, and of course the vocal arrangements in that insane break before the third verse. I could be wrong but it sounds like Brian had a bit to do with that song.
Indeed it does, however the basic track at least was in fact produced by Carl. Brian may have been involved with producing or co-producing the numerous vocal overdubs, though. To further answer your question, it appears Carl was the Beach Boy most involved with the mixdowns during those days (this from various sources, including Al and Desper).