Characterizing radioactive deposits in process piping is important for nuclear facility decommissioning and radioactive waste management, yet direct measurement of internal source distributions is often impractical. This study develops a constrained detector-placement method for reconstructing the relative strengths of multiple source regions from limited external measurements. Without access to the held-out source distributions used for evaluation, detector selection relies only on OpenMC response matrices, their Monte Carlo statistical uncertainties, and prespecified installation constraints. The method preserves information in the weakest observable direction while favoring layouts with greater overall information content. It is evaluated for straight, single-bend, and triple-bend pipe geometries, each containing seven source regions emitting monoenergetic 661.657 keV photons from Cs-137. Two independently generated Monte Carlo response sets are used separately for detector selection and reconstruction, and for observation generation and performance evaluation. This separation reduces the risk of overly optimistic evaluation associated with using an identical response matrix for both data generation and inversion. Reconstruction is performed using weighted non-negative least squares for 250 held-out source distributions, with 100 independent Poisson realizations for each distribution. For performance evaluation, the simulated measurements are scaled to a reference count level of 10,000, with background counts set to 20% of this level. Compared with engineering-uniform layouts, the proposed layouts reduce the mean relative L2 reconstruction error by 22.59%, 5.44%, and 52.21% for the straight, single-bend, and triple-bend geometries, respectively. The benefit depends on both geometry and source distribution, with the largest improvement observed in the triple-bend geometry. In the straight pipe, comparisons with layouts based on either information criterion alone are inconclusive, while the single- and double-hotspot families in the single-bend geometry show no stable improvement over the engineering-uniform layout. These results indicate that response matrices and their statistical uncertainties can guide detector placement without using the evaluation source distributions.