We report on the fabrication of a perovskite-based ((C6H5C2H4 - NH3)2 PbI4) planar microcavity with a technique of a top dielectric mirror's migration in liquid, avoiding the degradation of the perovskite material. This approach allows for increasing the cavity Q-factor, without degrading the fragile molecular material. Strong coupling of the perovskite exciton to both the cavity mode and the first Bragg mode is evidenced from angle-resolved reflectivity and microphotoluminescence measurements at room temperature; an efficient relaxation toward the minimum of the main polariton branch is observed. The measured quality factor is significantly increased compared to previous reports where a top metallic mirror was used, showing the decisive advantage of the present fabrication technique toward the achievement of stimulated effects and polariton lasing with perovskite materials.