I don't think high pressure blasting of the water reservoir is a good idea. Why not try a biological way? Put some bleach in there for about 15mins (say 1 part bleach to 9 parts water), it will kill and dissolve the fungus. Then you can drain it out/siphon it out. You can also use hydrogen peroxide or other oxygen bleach if you prefer.

If you keep getting recontamination, then you may have to flush the water line as well with bleach/oxygen bleach. This is what we do for medical water line.

I don't know if bleach will damage the paint, so thoroughly rinse/wash the affected area immediately. Bleach will cause exposed steel and aluminium to corrode, but it is readily dissolved in water and easily removed.