Perceptual sound matching (PSM) aims to find the input parameters to a synthesizer so as to best imitate an audio target. Deep learning for PSM optimizes a neural network to analyze and reconstruct prerecorded samples. In this context, our article addresses the problem of designing a suitable loss function when the training set is generated by a differentiable synthesizer. Our main contribution is perceptual-neural-physical loss (PNP), which aims at addressing a tradeoff between perceptual relevance and computational efficiency. The key idea behind PNP is to linearize the effect of synthesis parameters upon auditory features in the vicinity of each training sample. The linearization procedure is massively paralellizable, can be precomputed, and offers a 100-fold speedup during gradient descent compared to differentiable digital signal processing (DDSP). We demonstrate PNP on two datasets of nonstationary sounds: an AM/FM arpeggiator and a physical model of rectangular membranes. We show that PNP is able to accelerate DDSP with joint time-frequency scattering transform (JTFS) as auditory feature, while preserving its perceptual fidelity. Additionally, we evaluate the impact of other design choices in PSM: parameter rescaling, pretraining, auditory representation, and gradient clipping. We report state-of-the-art results on both datasets and find that PNP-accelerated JTFS has greater influence on PSM performance than any other design choice.