The island formula, derived from replica wormhole saddles in the gravitational path integral, successfully reproduces the unitary Page curve for black hole radiation entropy in the large- N (large central charge) limit. However, the resulting entropy profile contains an unphysical sharp kink at the Page time t Page—a mathematical artefact of the min operation that dominates in that limit. Any finite quantum system must exhibit a smooth, analytic transition. In this paper we work within Jackiw–Teitelboim (JT) gravity coupled to a holographic CFT bath and derive systematically the leading finite- N correction to the radiation entropy, $S_{\text{rad}}(t,N)=S_{\text{Hawk}}\left(t\right)+\delta S(N,t),\delta S\sim \mathcal{O}\left({\mathrm{e}}^{-S_{\text{BH}}}\right),$originating from non-perturbative interference between the Hawking and replica wormhole saddles. Using a soft-mode resummation of the gravitational path integral we show that these corrections replace the sharp kink with a log-sum-exp interpolation controlled by 1/ N. We further study an interference term arising when both saddles contribute at comparable weight, providing the first analytic description of a smooth cross-over in the island formula. Our predictions are confirmed by a random-unitary-circuit simulation of an n-qubit Page transition and by direct numerical evaluation of the partition function in a matrix-model truncation of JT gravity. The results imply that information begins to leak gradually from the black hole interior long before t Page, consistent with unitarity but without invoking a firewall.