You will never 'clean up' a dead-end filter such as this.
Whats probably happened is that bacteria have propagated and grown
'through' the filter media and are now totally blocking it ( to the
tune of 10,000,000 'bodies' per sq. cm). Buy new filter cartridges
and change out when they become 'slimey' to the touch - you will
develop a history of how fast the bacterial slimes form. A carbon
packed filter will enhance the multiplication of microorganisms and
needs to be changed more often.

To disinfect the filter housing, scrub with caustic (lye) soap, then
soak in strong Chlorox solution. Better to use peracetic acid, if you
can find it - as many microorganisms are unaffected by chlorine
disinfection. Since you probably have a major 'infection' dont follow
over-touted 'sanitization' steps as "sanitization" is used for a
'clean' system maintenance. The kill-rate of sanitization grade
chemicals will probably not 'budge' what you describe.
If the water hoses have turned 'brown' - replace them entirely; or,
they will continue to 'inoculate' the system with more micro-organisms
(spores). Many of these spores can be resistant to Chlorine/Chlorox.

Be careful of 'internet' disinfection and sanitization advice ....
usually quite obsolete and not applicable to a 'stagnant' water system
on a boat.