When the three positive horizons of a Kerr–Newman–de Sitter black hole coalesce, the separated perturbation equations lose the structure on which near-extremal quasinormal analysis rests: surface gravities vanish one power of the horizon separation faster than angular velocities converge. We prove that a mode synchronous at one horizon of a rotating q-fold cluster carries exponents of order aε 2−q at the others, so bounded horizon-frame exponents force a = O(ε), which approaches the static endpoint of the exact on-shell ultracold arc 2√3 − 3 ≤ Λs 2 ≤12. A vanishing-order theorem gives the Katz slope in all sectors, and the distinguished balance produces a resolved four-singularity Heun operator whose Coulomb fibre no physical harmonic occupies; fixed harmonics instead meet an ε−1 barrier between two imaginary-order modified-Bessel layers. For exact static and rotating families a = αh2 the normalized Evans function tends to one uniformly on compact scaled-frequency sets, so every fixed-harmonic neutral-scalar resonance obeys |ν| → ∞. The same architecture holds for the intrinsic Einstein–Maxwell perturbations: every radiative channel, in both parities, has throat coefficient L±√2L, even and odd coincide because of the triple root, and static escape holds. Under slow rotation a selection rule, a Schur bound and a three-check gate closure give a positive matrix barrier, and the matrix Bessel–Evans limit yields rotating escape at the same O(h2/3) rate. An independent full-harmonic contraction confirms that the first-order polar potential is regular, superseding a contrary July 2026 claim.