Photonic time-delay reservoir computing (TDRC) is an optical neural network structure known for its simple hardware implementation. However, this simplicity reduces information processing speed due to its sequential time multiplexing mechanism, such as the masking operation in practical experiments. To address this, we employ a deep photonic TDRC structure to enhance reservoir dynamics, effectively reducing the mask size to accelerate processing while maintaining high performance. An extended state matrix is proposed to leverage the enriched dynamics without additional hardware costs, combining different nonlinear intensities and memory lengths to augment node states without physically expanding the reservoir. Experimentally validated in a speech recognition task, our approach accelerates processing by 10 times with only a 2.4% decrease in recognition accuracy, compared to a 13.1% accuracy deterioration in the conventional scheme, indicating significant acceleration in TDRC information processing while maintaining performance.