Cleaning an overhead water tank using Alum or other chemicals?
Aluminum is remarkable safe for human consumption, also considering that it is present in high concentration essentially everywhere, and it is not known to have any significant specific biological roles. Wikipedia happens to have a nice well researcher section on aluminum's possible effects on human and animal health: Aluminium: health concerns. Alum is also routinely added to water in low concentrations for elimination of solid particulate, as you mentioned.

My main concern for your application is the fact that typical methods of water purification from solid particulate, just like addition of alum, will tend to form flocs in your water tank that will then need to be removed! Depending whether this scum will float on top of the water, or sink to the bottom of the tank, the removal may be more or less easy, also depending on what kind of access you have to this tank. I doubt if any of those solutions would count as not "doing much effort"...