Price-based management of distributed energy resources within microgrids is continuously gaining ground due to scalability and privacy limitations of centralized architectures. However, the concentration of flexible loads' response to the lowest-priced periods yields inefficient solutions. A previously proposed measure imposing a flexibility restriction on flexible loads might raise acceptability and feasibility concerns by the users. This paper develops a novel fully price-based approach where this hard restriction is replaced by a soft nonlinear price signal. This signal is customized to the operating properties of the different flexible load types by penalizing the square of the demand and the duration of cycle delay of loads with continuously adjustable power levels and deferrable cycles, respectively. This approach is shown to produce more efficient solutions than the flexibility restriction measure for both types of loads. For the latter type, randomization of the nonlinear prices brings additional benefits, especially in low operating diversity cases. These contributions are supported by case studies on a microgrid test system with electric vehicles and wet appliances used as representative examples of the above flexible load types.