CLR Flush

Based on your suggestion, I'm assuming I want to keep the gunk from the block out of the radiator and heater core.

Exactly.

If you do use it on your heater core, be gentle with the air, and be SURE you are blowing it backwards to flow the first rinse.

On the block direction does not matter since it does not have tubes that can be plugged up.
Just blast it both directions a few times.