Sounds like a classic case of electrolysis, though I've never come across it with a Northstar.
You can test for electrolysis with a DVM. Hook up the negative lead directly to the negative battery terminal, insert the positive lead into the surge tank, set the meter to DC volts and low volt range, start the engine and run it both idle and 2,000 RPM and check for voltage. If there's anything more than 0.3 volts, electrolysis is likely. Also check on AC volts.
Any aftermarket electrical crap in the vehicle?
The fix? Flush the coolant, check and clean all grounds, and retest. If there's AC voltage, a diode may be bad in the alternator. Also operate various electrical items while checking coolant voltage, if operating the item (aftermarket first) causes the coolant voltage to drop, you found a culprit.
When you found the problem, replace the heater core with a genuine GM part.
Joe