Recent Suzaku X-ray spectra of 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 supernova Type Ia. Varying the progenitor white dwarf internal structure, composition, ignition, and explosion mechanism, we find the best match to the observed iron-peak elements of 3C 397 are dense (central density $\geq 6\cdot 10^9$ g cm$^{-3}$), low-carbon white dwarfs 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 supernova Type Ia. A pure deflagration of a centrally-ignited, low central density ($\simeq 2\cdot 10^9$g cm$^{−3}$) progenitor white dwarf, 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 linewidth data. Additionally, in contrast to prior work which suggested a large super-solar metallicity for the white dwarf progenitor for SNR 3C 397, we find satisfactory agreement for solar and sub-solar metallicity progenitors. We discuss a range of implications our results have for the single-degenerate channel.