While many acoustic systems are well-modelled by linear time-invariant dynamical systems, high-fidelity models often become computationally expensive due the complexity of dynamics. Reduced order modelling techniques, such as the Eigensystem Realization Algorithm (ERA), can be used to create efficient surrogate models from measurement data, particularly impulse responses. However, practical challenges remain, including the presence of input-output dead times, i.e. propagation delays, in the data, which can increase model order and introduce artifacts like pre-ringing. This paper introduces an improved technique for the extraction of dead times, by formulating a linear program to separate input and output dead times from the data. Additionally, the paper presents an adaptive randomized ERA pipeline that leverages recent advances in numerical linear algebra to reduce computational complexity and enabling scalable model reduction. Benchmarking on large-scale datasets of measured room impulse responses demonstrates that the propsed dead time extraction scheme yields more accurate and efficient reduced order models compared to previous approaches. The implementation is made available as open-source Python code, facilitating reproducibility and further research.