2 thoughts:
1)Lincoln L water pumps generate considerable flow and pressure. A restricted radiator may cause pressure buildup. Even a clean radiator requires good gaskets and a good seal at the radiator cap.
2) Leak may be in the intake manifold, as it carries water and exhaust gas as well as fuel mixture. With modern gasoline, the exhaust passage in the manifold is unnecessary, even detrimental, adding to heat load on the carburetor. The exhaust passages into the intake manifold can be blocked by putting welsh plugs in the exhaust manifold ports. The little tubes that connect to the intake manifold can be put back in place without the seal rings, to maintain original appearance.