The Purkinje network plays a determinant role in the electrical activation sequence of the human heart. However, Purkinje properties cannot be clinically measured directly. Recent studies have successfully demonstrated cardiac digital twins without Purkinje networks, using inference methods integrating cardiac magnetic resonance (CMR) imaging and electrocardiogram (ECG) data. A sophisticated strategy to recover a patient's plausible Purkinje structure would enable these cardiac digital twins to augment clinical data and inform Purkinje-based risk stratification. This study presents and evaluates new computational techniques to infer physiological Purkinje terminal (root node) locations and timings and cardiac conduction properties from clinical CMR and ECG using Eikonal simulations. Our extended sequential Monte Carlo approximate Bayesian computation-based inference method shows an improved match in simulated QRS complexes to Q-wave morphologies in clinical 12-lead ECGs with Pearson's correlation coefficients of 0.89.