Regardless of what was, or was not, going on previously with the radiator....."the very bad noise heard 2nd time engine stopped" seems to warrant opening the engine further. ?remove cylinder head?
Show parts to forum or scooter shop to get ideas of causes, possibility of repairs, etc.
600 high speed miles on a 10 yr old 250 .....oil lubricity or coolant system failure, valve settings, spark plug heat range, cam chain, come to my mind.
Hang in there,
Stig