I have flushed my coolant 12+ times in an attempt to get pure water back out of the radiator. However, it still has a rust tint to it.
The reason is because I’m about to install new hoses and radiator and wanted a clean system before install.
Air pressure and water usually works the best. You can try chemical coolant flushes with rust inhibitors , but it’s likely you will never get all the rust out. Cause it’s going to be an every crevice it can find in the cooling system .
In my experience, once the inside of the block rusts due to neglect of cooling system maintenance, there's no going back. Sooner or later your new coolant will be rust colored again.
Only way I know to get rid of it is tear down the engine and have the block cooked out.
You're doing it the right way. There is no other secret method. Like the others have stated you'll most likely never get it all. Flush the heater core separately with a garden hose. Same with your current radiator. Remove top and bottom radiator hose and flush with garden hose. Hold your hand over the bottom, let the radi fill up, puke it out, repeat a few times. Obviously catch all the coolant first, don't go letting that junk dribble down the driveway.
Then once it's clear water, hook it all up, burp it, drive it, repeat until satisfied, then put your new stuff on.
Honestly it's overkill but if that's what you want to do, go for it.