I'd flush the cooling system first and then follow that up by separately flushing the heater core. Flushing the cooling system isn't normally effective at also flushing the heater core.
All radiators are 1 core, but they can have 1, 2, 3, or sometimes even more rows within that core. Whether 1 row or 3 rows is better depends on the application. For most Jeeping uses, a 1 row radiator is better because it has bigger water channels. The TJ began with a 2-row radiator, that's what mine came with, and later went to a 1-row radiator to give slightly better cooling characteristics. Did you also replace the thermostat? If not, be sure to only use the factory recommended 195 degree model thermostat. A 165 or 180 degree thermostat will just cause the engine to warm up more slowly while not helping the engine to run cooler on hot days.