I have been using the steradent trick for many years. If going down this route, don't bother removing the radiator, but instead keep it in place and run as follows:
Drain all coolant out of the system and flush through both the engine and radiator (seperately) a number of times. If possible, flush, then backflush, then flush the radiator and engine through. A few times if you can.
Reconnect the whole system, moslty fill with water then drop in a whole tube of steradent tablets. Allow them to dissolve and top up the system as normal.
Run the engine, bleeding the system if your engine has bleed points, top the water up again then let the whole system come up to temperature (ideally wait until the thermostat is open and the radiator really hot)
The engine and radiator should now have a nicely mixed steradent solution all around it. Leave the whole thing for 24hrs to allow the steradent to do what it can to the coolant system then flush the lot out the same as you did initially.
Once you're happy you've flushed it all out, refill, bleed and top up with the proper coolant/antifreeze mix and see how you get on.
I did have a radiator that was so clogged that steradent wouldn't touch it. I removed the rad and filled it with neat brick acid (I bought this from Wickes) and left overnight. The very next day I emptied the radiator and couldn't believe the sludge & curse word that came out of it despite having done my usual flush with water then steradent. The brick acid had broken down and dislodged SO much build up from the cores that the radiator could now take double the coolant it had before!!
Here is the radiator where you can see the cores (just) completely clogged with limescale and years of silt build up. This was AFTER flushing through for 24hrs with limescale remover.
Here is the brick acid doing its thing. There was a definite fizzing throughout the process as the limescale gradually dissolved.
However, this also highlighted that the radiator was past its sell by date because not only did it remove most of the crud that was blocking the cores, but it also opened up holes in the rad that were previously being blocked by the sludge and limescale. Brick acid won't corrode the brass of the radiator itself, so wasn't resonsible for creating the leaks but as a byproduct of removing all the debris and limescale, also showed that the radiator was beyond its best.
I ended up having the radiator recored and the difference was immense! I could see how much debris was still in the old cores despite the sterdaent THEN brick acid flush..and despite seeing how much crud came out of the radiator.
Basically, if your radiator is old enough and clogged enough to need flushing, the chances are it's possibly going to need replacing, but give it a go with some treatments first because it might just be good enough to revive without ending up with a sieve.
Here's a video of some of the sediment that came out of the radiator after leaving brick acid in it overnight (most of the horrible sludge had already been poured out before I thought to video it)
Here is what I was greeted with once the newly flushed out radiator was refitted. This led to paying for a recore...which was less than ideal, but such an improvement that I'm glad I did now.