The core is very likely bad like they are saying. Be sure they have the ability to use your old top and bottom rails as well as the original tanks. Some radiator shops can’t do this. My radiator shop can order cores without the rails and reuse the originals. On the one I just had done for my 4 speed car they sent the rails to the core manufacturer and they made the core right to my original rails. I will have to look more into the hood insulation, I can’t remember much at this time and will have to look at my old pictures when I get time. I do remember that that new pad has that little spot perforated to where it can stay or be cut out.