The artificial gauge field for electrically neutral exciton polaritons devoid from the polarization degree of freedom can be synthesized by means of applying crossed electric and magnetic fields. The appearance of the gauge potential can be ascribed to the motional (magneto-electric) Stark effect which is responsible for the presence of a linear-in-momentum contribution to the exciton kinetic energy. We study the interplay of this phenomenon with the competing effect which arises from the Rabi-splitting renormalization due the reduction of the electron-hole overlap for a moving exciton. Accounting for this mechanism is crucial in the structures with the high ratio of Rabi splitting and the exciton binding energy. Besides, we propose an approach which boosts the gauge field in the considered system. It takes advantage of the crossover from the hydrogen-like exciton to the strongly dipole-polarized exciton state at a specific choice of electric and magnetic fields. The strong sensitivity of the exciton energy to the momentum in this regime leads to the large values of the gauge field. We consider the specific example of a GaAs ring-shape polariton Berry phase interferometer and show that the flux of the effective magnetic field may approach the flux quantum value in the considered crossover regime.