I've wondered about putting a tank on the 2nd floor of the house. (Like a

This is exactly what the third world countries do (except the tank is on the
roof). Large cities do not have a good water system, so they "rotate" water
pressure around the city. Your house might get water for 8 or 16 hours a
day, for example.

These places have one or two reservoirs on top of the house, all the water
into the house (and the water heater, etc..) comes from the reservoirs. The
rich people have an additional underground reservoir that feeds the
reservoirs on the roof through an electric pump (either manually or
automatically operated). This is a lot of water that gets stored!

With a properly-designed system (you'd have to hire a 3rd world engineer,
but they really have the physics of this down), you can get a decent
gravity-pressurized water system. The water pipes have to be sized and
routed correctly.

--
gabriel