Transition to sustainable energy origins, carbon-neutral energy carriers and leaner-burning combustion concepts is strongly discussed for its prospective role in greener and secure energy future. Polyoxymethylene dimethyl ethers (PODEn), well-suited for compression-ignition combustion modes, are considered as potential carbon-neutral candidates. To elucidate their potential, a detailed knowledge of lean PODEn combustion characteristics, as well as underlying chemical kinetics, is necessary. In this paper, numerical insights into multi-stage heat release peculiarities of PODE1/oxidizer propellant pertinent to lean spontaneous auto-ignition, are presented and compared to n-heptane. Macro-dynamics of three-stage heat release (3SHR) phenomenon, earlier revealed by the authors to predominantly occur at low-to-intermediate initial temperatures (below 900 K) at ultra-lean conditions (equivalence ratios (φ) below 0.5), is discussed. For this task, initial-state sensitivity analysis of the heat release rate (HRR) characteristic parameters (e.g., peak amplitudes, proximities), was conducted. Detailed PODE1 kinetic mechanisms, formerly identified as the most accurate for lean PODE1 autoignition, were utilized for constant-volume adiabatic reactor simulations at initial temperatures of 600-900 K, pressures of 10-40 bar, and φ = 0.1-0.5. Results revealed distinct perturbing effects of initial-state parameters on 3SHR macro-dynamics, sensed through raw and logarithmic derivative profiles of peak proximities and amplitudes. PODE1 and n-heptane showed several contrary results attributed to dissimilarities in negative temperature coefficient (NTC) behavior.