Yeah, it's a bit of project. Not hard, by any means, just time consuming. Since you just got the boat, once you get it clean, just make it a habit to keep the water system clean in the future so you don't have to deal with this again. A little preventative maintenance goes a long way.
You might start with just letting a blach/water mixture (a cup of bleach is plenty) set in the tank for day, first. And go trailer it around for a bit to agitate things. I wonder if you couldn't stick a hose down the fill neck, to the bottom of the tank? Duct tape that hose to a shop vac hose. Maybe you'll get rid of a good majority of the crud that way. Once you get the tank mostly clean, do another water/bleach mix and pump it through the entire system and again let it sit for a while.
Depending on your access to the fresh water pump, and it's filter (to keep cleaning it), disconnect the output side and run it into a bucket or just into the bilge. If that's easier for you to help get the majority of the crud out, that is.
Ever see those water hose end fittings (for garden hose) that have little holes in them? I wonder if you couldn't snake that down through the fill hose? They're sort of like little pressure washer nozzles. Maybe you could do the same thing by inserting a barb to barb fitting in the end of the garden hose, then plugging the free end of the barb fitting and drilling small holes in it (experiment with size). If that fits into the tank, it should do a better job of dislodging the crud.