I've always thought that "big block 350" was a misnomer for the Pontiac motors. Apparently, GM's Pontiac motors were configured differently from Chevy and Buick. I've also heard the Pontiac motor referred to as a so-called "medium block".
I used to have a 61 Impala SS. Some of the 60s Impalas did have a 348 motor with 350hp. Maybe that's part of the confusion.
Someone else would have to tell you if GM crossed over any Pontiac 350s to Impalas in the 60s. I do not know.