Surely the mucky water can be replaced with clean water by simply
flushing?
I do my 23 year old solid fuel system every two years. Turn all
radiators OFF except one, turn pump on high speed and continually drain
the system. Do this sequentually around the house starting upstairs. It
takes a week or more for the water to become de-aireated again but
generally that only effects the upstairs radiators.

Chris.