I am a total noob but your mention of sticking a brush in the tank reminded me of something. At a martial arts school I went to they had a water cooler with a 5 gallon plastic water container on top that they would refill rather than have a service replace. After awhile it would get pretty slimy on the inside and to clean it they would put ice cubes in it with soap and swirl it around. Worked very well and the ice could just be dumped out.
I can imagine the tank you are talking about is much bigger and would require some engineering to "swirl" it but most any problem involves trading off time and money and hey it could be fun.