Our objective is to invert for large 3-D salt models using full-waveform inversion (FWI), especially in the absence of good starting models and low frequencies in the seismic data. This objective incurs a couple of critical issues. First, the presence of salt geobodies aggravates the non-linearity and ill-posedness of FWI. Second, a 3-D FWI is computationally very expensive, even more so when the initial model is in hindsight very far from the target one. To mitigate the ill-posedness, we propose to utilize model regularization in the FWI framework to promote a limited variation in the inverted model followed by a post-processing step of FWI to penalize sharp velocity drops in the model. Next, to reduce the computational overburden, we propose to utilize a multi-excitation assumption (MExA) of source wavefields in the FWI gradient calculation step. This assumption, due to the simplistic nature of the source wavelet, approximates the source wavefield wiggle at a gridpoint by a series of its energetic arrivals. As a result, the gradient evaluation using MExA requires us neither to store the entire source wavefield nor to include an additional extrapolation step to propagate the source wavefield from its temporary storage at the boundary. The versatility of the proposed method is demonstrated on a synthetic dataset of the modified SEG/EAGE salt model in which the lowest available frequency is 3 Hz.