Edge illumination is an emerging X-ray phase contrast imaging technique providing attenuation, phase and dark field contrast. Despite the successful transition from synchrotron to lab sources, the cone beam geometry of lab systems limits the effectiveness of using conventional planar gratings. The non-parallel incidence of X-rays introduces shadowing effects, worsening with increasing cone angle. To overcome this limitation, several alternative grating designs can be considered. In this paper, the effectiveness of three alternative designs is compared to conventional gratings using numerical simulations. Improvements in flux and contrast are discussed, taking into account practical considerations concerning the implementation of the designs.