Getting some miles on it will help a lot, 500 to 1k will let all parts mate where there is no more excess heat from friction of a new engine.
These cars were originally built to not "require a break-in period before they wouldn't overheat". If there is THAT much "friction" in the cylinders and/or clearances that the engine labors excessively, or enough to cause an overheating condition, I would call that a poor rebuild job. I don't think I am alone on that opinion.
What is the history of the radiator before going and modifying the car
Good question and a great place to begin before choosing to modify your car away from original. Ford did not engineer these cars to operate with add-On's (such as air conditioning), at least not in extremely hot climates. When AC was added, then it would be typical to need upgrades, even on Dealer Install jobs. Otherwise, what was installed on the cars, was adequate to the typical conditions found in most locations.
Let me ask instead another question related to the O.P's initial statement of "Overheating".
Did the car overheat on the gauge? Blow steam and coolant everywhere? Or, did the car simply push out some coolant while waiting in the line?
Reminder: Since these cars were not designed with a Coolant Overflow System, the upper radiator tank doubled as an Expansion Tank and often, as long as the coolant level was over the tubes of the radiator, the cooling system was considered "FULL". I would hope with all your hard work, that perhaps the radiator just was a little over-full.
