If the radiator is that clogged, shop for another one...... ( BTW) It cost me $90 to flush mine.
They could put in a new core......
Uh, if you do flush it, be sure to plug the oil fittings, but check the radiator after it's flushed, when you install it, and it's supposed to be hot, lay your hand on it in different locations and see if there are any cool areas. ( areas still clogged )