I had a very similar situation with my 67. The car was fine when it was moving, but if I sat still all hell broke loose. I tried a ton of things. 4 core radiator, different thermostats, messing with the timing, assorted deities, and for me it turned out to be mostly the water pump diverter plates.
basically Pontiac made water pumps with large impellors that would spin really close to the diverter plates and create a good bit of suction to move the coolant around even at low RPM. Unfortunately, a lot of aftermarket water pumps have much smaller impellors and the gap between the diverter plate and impellors is too great to move adequate coolant when RPMs are low. For me I just bought new diverter plates ( I think there are 2 plates on 67's, your may be different like the one pictured in the link below) and then popped a new water pump on. I checked the clearance and hooked everything back up. It made a horrible screaming noise since I had it too close, so I took it apart again and adjusted a bit, and then it fit fine. Now she runs much better. If your using an aftermarket water pump, I would wager this is like 80-90% of the problem. Follow this link for a better idea of what I'm talking about.
