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Recent Suzaku X-ray spectra of supernova remnant (SNR) 3C 397 indicate enhanced stable iron group element abundances of Ni, Mn, Cr, and Fe. Seeking to address key questions about the progenitor and explosion mechanism of 3C 397, we compute nucleosynthetic yields from a suite of multidimensional hydrodynamics models in the near-Chandrasekhar-mass, single-degenerate paradigm for Type Ia supernovae (SNe Ia). Varying the progenitor white dwarf (WD) internal structure, composition, ignition, and explosion mechanism, we find that the best match to the observed iron peak elements of 3C 397 are dense (central density ≥6 × 109 g cm−3), low-carbon WDs that undergo a weak, centrally ignited deflagration, followed by a subsequent detonation. The amount of 56Ni produced is consistent with a normal or bright normal SNe Ia. A pure deflagration of a centrally ignited, low central density (≃2 × 109 g cm−3) progenitor WD, frequently considered in the literature, is also found to produce good agreement with 3C 397 nucleosynthetic yields, but leads to a subluminous SN Ia event, in conflict with X-ray line width data. Additionally, in contrast to prior work that suggested a large supersolar metallicity for the WD progenitor for SNR 3C 397, we find satisfactory agreement for solar- and subsolar-metallicity progenitors. We discuss a range of implications our results have for the single-degenerate channel. [ABSTRACT FROM AUTHOR]