This work focuses on accelerating and stabilizing Physics-Informed Neural Networks (PINNs) for the solution of high-frequency wave propagation problems, with particular emphasis on the scattered Helmholtz equation. Despite their theoretical appeal, conventional PINNs often struggle in this regime due to spectral bias, poor representation of oscillatory solutions, and severe optimization difficulties that lead to slow or stalled convergence. To address these challenges, we propose a hybrid framework that introduces innovations at both the architectural and optimization levels. From an architectural perspective, we embed Gabor-inspired basis functions directly into the neural network, enabling an explicit and adaptive representation of localized oscillatory patterns inherent to scattered wavefields. This design significantly enhances the expressive power of the network for high-frequency solutions without requiring excessive depth or width. From an optimization standpoint, we incorporate a least-squares (LS) solver within the training loop to analytically optimize a subset of network parameters while the remaining parameters are updated via gradient-based methods. This LS-embedded optimization reduces the stiffness of the loss landscape and leads to substantially faster convergence compared to standard PINN training. Numerical experiments on scattered Helmholtz problems in strongly heterogeneous media demonstrate that the proposed approach achieves higher accuracy, improved stability, and reduction in training time relative to classical PINNs. The results highlight the importance of jointly designing neural architectures and optimization strategies for efficient PDE approximation in high-frequency regimes.