Geometry-reconfigurable arrays offer additional spatial flexibility for cell-free integrated sensing and communication (ISAC), but unknown complex bistatic gains can limit their localization benefit. We derive a nuisance-aware equivalent Fisher information matrix that isolates identifiable angular information after gain elimination. The analysis shows that rank-one probing provides no transmit-angle information, even when a known-gain model predicts a positive value; rank at least two is necessary but not sufficient. Mapping angular information to position separates local aperture sensitivity from network angular diversity. We then jointly optimize communication and probing covariances and transmit/receive array shapes using semidefinite covariance optimization and safeguarded shape search, with deterministic rank-one recovery of communication covariances. A hybrid information model incorporates residual orientation and actuator errors to characterize calibration limits. Under a physical 28-GHz model, joint reconfiguration achieves a 5.51-dB paired Cramer-Rao bound gain over collapsed-geometry covariance-only design across 48 trials. Maximum-likelihood localization remains within 0.45 dB of the root-mean-square position error bound at the tested efficiency points. Orientation uncertainty substantially degrades localization, while covariance robustification offers little improvement in the evaluated setting. These results identify when geometry reconfiguration yields localization gains and how residual calibration errors limit their realization.