So, is this when you are just cruising or just trying to slowly accelerate, or when you are at 65 MPH and then punch it? If this is happening under cruise conditions then it won't be the secondaries; the engine will be running on the primaries at the point if cruising on flat land. And this is not the accelerator pump if this is at steady speeds.
(BTW, if you have a vacuum gauge in the car, you can get a pretty good idea of what phase of carb operation is going on with vacuum readings.)
The suggestion of the plugged fuel system is most likely. Be ready to pull the tank and clean or replace it. At this car's age, the tank and lines are suspect. It can get into the fuel pump's check valves and muck that up, as well as into the carb. If you don't know if this has been done by a PO, it is time for a full fuel system cleaning. THIS HAPPENS ALL THE TIME TO THIS VINTAGE OF CAR.
BTW, with a 20" vacuum at idle, the cam is not big. So a 650 is fine. I ran a 351C to 6500 RPM all day long for years and years on an old Holley 1850 600 cfm.
