Recent advances for silent MRI have shown that spatial encoding can be achieved using RF rather than linearly varying static magnetic field gradients. This has been demonstrated using homogeneous transmit (B1) fields with linearly varying phase gradients. Similar results can be achieved with linear B1 amplitude gradients with homogeneous phase. The efficacy of either method is limited by a maximum B1 gradient strength (phase or magnitude) per specific absorption rate. Here we demonstrate a novel approach to relieve this restriction where highly nonlinear B1 gradients can be used for combined amplitude and phase modulation with reconstruction using state-of-the-art machine learning models.