Repeated observations of one physical object need not constitute independent channel uses. We model partial nanopore protein rereads as a finite-alphabet channel with canonical content, persistent readout, and pass-local coverage and synchronization. For exact compound-pass data, matched inference approaches the equivalence-class canonical posterior, and sitewise excess Bayes risk admits an action-aware achievable exponent. In an aligned specialization, observation-local redraw can cause linear-in-$K$ growth in true-label negative log-likelihood (NLL). We derive order-$b$ projection-stability bounds and an exact passwise-fusion diagnostic. On a PASTOR-informed semi-synthetic hard-symbol channel, label-blind deterministic-mixture importance sampling (LB-IS) agrees with exact enumeration at $L=7$. At $L=24, K=10$, LB-IS meets every prespecified aggregate absolute marginal-posterior and score-agreement criterion against a fixed high-allocation reference in three selected conditions. Joint agreement holds for the representative and high-NLL conditions, while the near-zero condition remains inconclusive. Exact $L \leq 6$ benchmarks identify order 4 as the smallest tested common cap. At target scale, the reference supports selected unprojected functionals, while neither order 4 nor 5 attains joint agreement, defining a tested finite-memory boundary. Across 16 cells, the order-4 shared branch lowers NLL by 0.033-0.224 nats per residue relative to pass-local.

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