Well, there ya go! Very fortunate to get such detail from the son.
Now that you know about the Aquatennial, you can start searching for some pics of the parade. With so many people about it must have made it into some pics. I just had a quick look and saw mention that Jefferson Airplane were there that year, maybe they got to ride in your car?
I tracked down the original owner of one of my cars and his response was "Oh I owned lots of cars over the years (like he couldn't remember owning a GTO!!), good luck with it" and then ended the phone call.