Adaptive control of linear systems with unknown nonminimum-phase (NMP) zeros remains a significant challenge. Although retrospective cost adaptive control (RCAC) is applicable to NMP systems with known NMP zeros, errors in the knowledge of those zeros can lead to unstable pole/zero cancellation under sufficiently aggressive tuning. To address this problem, this paper provides a numerical investigation of a heuristic extension of RCAC that exploits the propensity of RCAC to cancel NMP zeros, thereby inferring the NMP zeros. This modeling information can be subsequently incorporated within the target model used by RCAC. By focusing on only NMP zeros, this approach is distinct from conventional system identification, which relies on input-output data for model fitting. This cancellation-based technique relies on saturation of the control input and instability of the feedback controller. Simultaneous occurrence of control saturation and controller instability provides a heuristic indicator that the controller has cancelled one or more NMP zero during closed-loop operation. The estimated NMP zeros are subsequently used within a cancellation-based pseudo-identification extension of RCAC to prevent further cancellation of the NMP zeros.