I replaced my water pump just as a precaution, but I doubt that's your problem. Here's how 'd approach it: First, verify your gauge is accurate. If it's not puking coolant out at shutoff, it may not be as hot as you think. Buy a laser heat gun. Harbor Freight
https://www.harborfreight.com/121-infrared-laser-thermometer-63985.html
has them for cheap and they're accurate. Let your car warm up and take a reading off the upper radiator hose near the thermostat. It should be at or near the same as your gauge. If not, buy a new sending unit or gauge.
Next, check the thermostat. They are cheap and easy to replace and have been known to fail.
I also gotta ask, what was the condition of the coolant you drained before the radiator swap? If it was horribly rusty, has chunks in it, or anything else, then yeah, that's going to need a flush.
Are you using electric fans? If so, don't make the common mistake of putting them in front of the radiator, that actually blocks airflow.
Mine has no shroud, a stock, non-clutch, non-flex fan and I've had the car idling in 100+ degree traffic and the needles not been over halfway on the stock gauge.
Also, make sure your timing and carb are tuned correctly. Get the timing wrong and all the radiator in the world won't keep it cool under load.