The solutions using internal pressure, standpipes, heavy liquids, etc., can be done on very small tanks, but they aren't really needed there, either. On a tank of any size, it is impractical to pressurize the roof to achieve significant increases in pressure in the fluid. Purchase and disposal of any other heavier product would be very expensive on a tank of any size as well. If the tank includes a corrosion allowance, it would make it that much harder to stress to the design level. Additionally, when the product is heated, as sulfur, the design conditions can't be duplicated using products at ambient temperatures.
Normally such tanks will be built and hydrotested like any other tank. If additional safety is desired, it would make more sense to specify a lower design stress, a decreased joint effiiciency for design, or increased radiography, rather than going to great lengths to overstress the shell.
The API-650 hydrotest is not intended as an overstress proof-test as is done with pressure vessels. API limits the amount of overstress by specifying the allowable hydrotest stresses, but does not require that these stresses be reached in order to properly hydrotest a tank.