I probably did the totally wrong thing, but I used some paint
solvents, Mineral Spirits, along with one of the brushes
with very long metal shafts that are sold for cleaning
out clothes dryer lint traps. The long flexible brush shaft allowed me to bend it as necessary to get into all the far corners and scrub the tank with the solvents sloshing around. When I drained the solvents they brought out the gunk along with them.