If it goes white hot in just a couple of blocks and you are full of coolant, it almost has to not be moving water. I assume steam shoots out and the whole works right? Not just the temp gauge or light saying its hot.
Try turning the heater on high. Do you get lots of heat?
Let it get cool, take off the radiator cap, make sure its full to the top with coolant, and then crank it and let it idle while you watch the coolant. Don't Stand in the Line of Fire!!. If the coolant just sits there and then suddenly shoots out, the thermostat is messed up. The coolant should move up and down a few times as the engine warms up and then you should see some circulation. Feel the hoses. after it warms up they should both be warm all the way. If you do not have any heater heat, more than likely you do not have any water circulation. Either because of no water in part of the block or a water pump problem. A lot of newer cars can get an air bubble in the block and have special ways of filling the cooling system to prevent that. But I don't remember ever seeing a 350 do that.
However, I have once seen a water pump that the impeller was not on well. It would pump fine for a while, but after it warmed up, the impeller would expand slightly and start slipping on the shaft. At least that is the idea I am going with. The darn thing looked fine when I pulled it, and the impeller was tight. But, when things got warm, it quit pumping. A new one fixed it.
I have also seen a rebuilt water pump have the wrong impeller on it. But that one did not work right out of the box.
I have also see radiator hoses come apart inside and let a flap of rubber hang down and block flow intermittently.
Also, the radiator should be hot all the way up and down. if part of it is cold, you have a blockage. I don't know what would be blocked since its new, but you never know.
J.