I think there was a change with production date.
My brother's '65 Skylark and my father-in-law's '65 Skylark were both the 2 bbl engines and they had cross flow radiators. I have seen many '65 Skylarks with down flow radiators also. I have never looked at the production date on cowl tags though.
So, my point is that 2 bbl vs 4 bbl isn't a decider.
Loren