Reconstructing magnetization textures from nitrogen-vacancy (NV) magnetometry stray-field measurements is a challenging, fundamentally ill-posed inverse problem, further complicated by the unknown effective distance between sensor and magnetic material. Here we show that incorporating a micromagnetic energy functional directly into the inversion filters out unphysical, high-energy configurations, while Fourier-space upward continuation of the stray field allows us to simultaneously fit the distance. Applied to measurements of the van der Waals ferromagnet Fe₃₋ₓGaTe₂, it recovers an effective distance estimate of approximately 81nm and low-energy configurations that reproduce the observed field. More broadly, embedding physics directly into the reconstruction turns ill-posed magnetic inverse problems into transparent, interpretable reconstructions, with applicability well beyond NV magnetometry.