YOU SHOULD BE ABLE TO HAVE THE CURRENT RADIATOR REPAIRED....
....if it is an all metal one.
It is best, whenever possible, to have the original radiator cleaned, flow tested, and repaired. Most of the original radiators are copper and brass. Much more durable than the aluminum/plastic radiators in the aftermarket. One of those would not hold up in this car. These Lincolns did run "cool". On a 95 degree day, with A/C on, the temp gauge never hit the center mark.
I had a '63 and had the radiator repaired, as well as the overflow tank. I did have to remove the hood to remove the radiator, in order to get access separating the A/C Condenser from the Radiator. After repairing both, I never experienced any other Coolant leaks. One thing to remember with the old cars, is Never use any extended coolant, of any type, in them. Only use conventional Ethylene Glycol Coolant.
If you can find a repair shop that does Truck or Industrial Radiators, Gas tanks, etc., you should be able to have them repair your radiator. I use a local Industrial Radiator shop now to do any repairs on my Fury cooling system. They actually took the Original Radiator and converted it to 3 Rows from 2. Cleaned, flow tested and painted it. They reconditioned the fuel tank, as well.
Good luck with your repair. Feel free to write if you have any other questions.
Louis