This article describes an original approach to analyze simultaneously cross sections and surrogate data measurements using efficient Monte Carlo extended $\mathcal{R}$-matrix theory algorithm based on unique set of nuclear structure parameters. The alternative analytical path based on the manifold Hauser-Feshbach equation was intensively used in this work to gauge the errors carried by the surrogate-reaction method commonly taken to predict neutron-induced cross sections from observed partial decay probabilities... Present paper emphasizes in particular a dedicated way to treat direct reaction entrance and prior decay excited nucleus outgoing channels widths correlations. Present smart theoretical foundation brought the opportunity to apply successfully our method to both fission-probability data and directly measured neutron cross sections according to Pu fissile isotopes; namely the $^{237, 238, 240, 242~and~244}$Pu$^*$ nuclei. This new capability opens genuine perspectives in matter of 'evaluation process' from foreseen fission- and $\gamma$-decay probabilities simultaneously measured as derived data will become available. (read more)