Sparsification via neglecting far-field coupling (S-NFC) enables fast full-wave radar-cross-section analysis of large-scale chaff clouds by retaining only significant local electromagnetic interactions. This letter further accelerates S-NFC by concatenating the retained off-diagonal interaction blocks associated with each receiving chaff element and applying a joint low-rank factorization with a shared receiving-side basis. Exact self interactions are preserved, while repeated chaff templates reuse precomputed lower--upper factorizations of the self-interaction blocks. The compressed formulation reduces retained-coupling storage and matrix--vector multiplication cost and also decreases the number of iterations required by the generalized conjugate residual solver. Numerical tests with 100,000 chaff elements demonstrate sub-$1\%$ complex-far-field error for low-rank approximations in sparse regimes and identify a practical self-only limit at sufficiently large mean spacing. For a one-million-chaff plume, the proposed compressed S-NFC achieves a $6.92\times$ end-to-end speedup over uncompressed S-NFC while storing only $6.60\%$ of the retained coupling, with a complex-far-field error of $0.253\%$.

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