I have a local radiator shop that can re-core the radiator, if necessary. They won't give me a price over the phone - they want to see the radiator. I'll probably remove it from the truck and take it over them to get an estimate.
It has corrosion on sections of the core and the leaks were in the core, but they were minor. As previously stated, cooling system seal tabs stopped up those leaks (but I don't know how long this repair will last).