All radiators hot at the top and cold at the bottom

sludge, you could have a power flush done on system, or you could just add chemical cleaners yourself.

System needs a powerflush . Heavy sludge sinks to the bottom of the radiator

You cannot just add a cleaner, it needs professional knowledge and experience to determine the level of treatment required, A powerflush with appropriate chemicals to break down the sludge and mixture of metals(magnetite)will always be the best course. You could change out all the radiators but you will still need to powerflush out the pipework especially if it is plastic pipework or live in a hard water area, you would need additional chemicals such as a biocide.

In addition to the comments provided, would definitely recommend having a magnetic system filter fitted, as this will catch a lot of dirt of of your system in combination with the chemical cleaner.