The basic physics of sound waves enables ultrasound to visualize biological tissues with high spatial and temporal resolution. Recently, this capability was enhanced with the development of acoustic biomolecules - proteins with physical properties enabling them to scatter sound. The expression of these unique air-filled proteins, known as gas vesicles (GVs), in cells allows ultrasound to image cellular functions such as gene expression in vivo, providing ultrasound with its analog of optical fluorescent proteins. Acoustical methods for the in vivo detection of GVs are now required to maximize the impact of this technology in biology and medicine. We previously engineered GVs exhibiting a nonlinear scattering behavior in response to acoustic pressures above 300 kPa, and showed that amplitude-modulated (AM) ultrasound pulse sequences that both excite the linear and nonlinear GV scattering regimes were highly effective at distinguishing GVs from linear scatterers like soft biological tissues. Unfortunately, the in vivo specificity of AM ultrasound imaging is systematically compromised by the nonlinearity added by the GVs to propagating waves, resulting in strong image artifacts from linear scatterers downstream of GV inclusions. To address this issue, we present an imaging paradigm, cross-amplitude modulation (xAM), which relies on cross-propagating plane-wave transmissions of finite aperture X-waves to achieve quasi artifact-free in vivo imaging of GVs. The xAM method derives from counter-propagating wave interaction theory which predicts that, in media exhibiting quadratic elastic nonlinearity like biological tissue, the nonlinear interaction of counter-propagating acoustic waves is inefficient. By transmitting cross-propagating plane-waves, we minimize cumulative nonlinear interaction effects due to collinear wave propagation, while generating a transient wave-amplitude modulation at the two plane-waves' intersection. We show in both simulations and experiments that residual xAM nonlinearity due to wave propagation decreases as the plane-wave cross-propagation angle increases. We demonstrate in tissue-mimicking phantoms that imaging artifacts distal to GV inclusions decrease as the plane-wave cross-propagation angle opens, nearing complete extinction at angles above 16.5 degrees. Finally, we demonstrate that xAM enables highly specific in vivo imaging of GVs located in the gastrointestinal tract, a target of prime interest for future cellular imaging. These results advance the physical facet of the emerging field of biomolecular ultrasound, and are also relevant to synthetic ultrasound contrast agents.