[en] This article describes an original approach to simultaneously analyzing cross sections and data obtained with surrogate reactions, using an efficient Monte Carlo extended R-matrix theory algorithm based on an 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 infer neutron-induced cross sections from observed decay probabilities. The present paper emphasizes in particular a dedicated way to treat ingoing direct reaction and outgoing channels widths correlations and to recall the common absence of class-II states width fluctuation factor in standard codes for calculating average fission cross sections. The present approach opens interesting perspectives on the matter of neutron cross section inference as simultaneously measured fission and gamma-emission probabilities become widely available. (authors)