I have a bit of a background in small steam boilers, fittings and such…
what we do to clean out check valves and the like is disassemble them and let them soak in white vinegar for a few hours…
How about using a solution of white vinegar and water, warmed up, fill the radiator(cap the bottom of course), slosh it about, and let it sit such that all the crud settles by the lower radiator hose, them wash it out with warm water to flow the crud out?
might work… I dont see why not…
With the boilers we also use a teaspoon of ginger in the boiler fill to seal small pinhole leaks. this is effective as the operating pressure of the boiler is around 80-120 psi…
but I digress… think the vinegar solution might work?