what would grounding the heater core do?
the engine is grounded. assuming the antifreeze mix is conducting electricity, then the heater core should automatically be grounded by the coolant which flows into the metal engine and also the metal heater core. if you had poor grounds thet are eroded out to the point where the engine is trying to ground through the antifreeze in the heater core, then i could maybe see this happening, but by that time i doubt youre car would start.
one way to tell if you are getting electrolisys is to open up the cooling system and inspect the radiator, heater core, and engine block for plating. 1 of those 3 items will be very clean, becuse the metal is being wisked away to be plated into another item. sence you say it is the radiator which fails, see if you can look down one of the radiator passages for a rough erosion look. almost like the metal was sand blasted. it would be very clean but very rough.
if this was really happening, then the radiator should be eroding away and its metal would be deposited elsewhere, maybe into the engine passages, or maybe the heater core.
i still doubt this happens though. you need a strong electrolyte for electroplating to happen. it just doesnt happen with antifreeze. think of how saltwater outboards have that zinc anode, yet freshwater outboards dont have it.
did anyone see the mythbusters episode where they dealt with electrolisys? it took them 100 days to dissolve a 1 inchn thick iron bar using a transformer out of a big radio and salsa for electrolyte.
bottom line, check youre engine and battery grounds. if you are really convenced you are still having electrolisys and its keeping you awake, then run a little wire from the heater core to a ground. and one from the radiator to a ground.
you cant really do any more than that.
