I am going to stick my neck out a bit and say that first, it's not that bad, second a serious and time consuming effort may get only moderate results and finally, if you have a year of patience you'll see improvements by staying with a 'program' of treatments.
I've had good luck with using moderately strong concentrations of bleach (about 6 ounces in a tank fill-up) every third or fourth time I add water.
Having said that, living aboard we go through 1,000 liters pretty quickly when dockside.
After each "shock" the water smells strongly of chlorine for a day or two. That's when it's time to wash the sheets :)
The next fill-up is plain water, and may still smell of chlorine very slightly depending on how far down we depleted the tank.
Only on the third fill will I then flush the watermaker. After that I'll add 1/4 tsp of the StarBright water purifier.
Then the next one is plain water, then the next one (or one more if I lose count) is back to bleach. It works out to about monthly to bi-monthly.
The bleach treatments will kill a charcoal water filter quickly so I just use paper/fiber ones.
I also believe that if we were to highly chlorinated water sit in the lines it would be detrimental to pumps and valves and especially the copper fittings (nipples) on the holding tanks, so we always make sure we use the "bleached tank" of water fairly quickly.
Give it two years and see :)
SM 209, Adagio