I've got one of those hose nozzles with the graduated nozzle for different size hoses. I probably haven't use it in 30 years. It also has a port for an air hose. I was planning on using it on the heater core...
I have used one of those power back flushing tools for years. One suggestion. Be very careful if you use it on the heater core or you may be replacing the core. These are 40 years old and some are very weak. I have ruined a couple of them by applying a burst of air pressure. Just use the hose pressure and you should be fine.
We always take out the thermostat and reinstall the radiator hose. Disconnect the other end at the radiator and insert the tool. Disconnect the lower hose and back flush the block first. Then reconnect the lower hose and flush again. This back flushes the radiator also. But do the block first so that you don't force all of the crap from your block into the bottom of your radiator.