Split-prime supercongruences at a mixed CM point: order drop, Eisenstein dichotomy, and unconditional mod p² closure

Symmetric-cube hypergeometric coefficients at the mixed CM point (1/6, 1/3; 1) exhibit a clean arithmetic dichotomy governed by splitting in the Eisenstein decomposition of the logarithmic derivative. At split primes both Eisenstein pieces share the same local factor and the p⁴-tower survives; at inert primes a unit-root obstruction kills it. We prove by explicit counterexample that the natural bivariate congruence on the full Eisenstein module is false, while the congruence survives on the diagonal determined by the mixed combination Cₘix = C₀ − 27uC₀ — the unique Fricke-trace direction. The Hecke operator Tₚ commutes with the Fricke involution exactly at split primes, yielding an exactly w-invariant Hecke defect. A finite reduction (Proposition 13. 1) shows that the full transport cancellation conjecture is equivalent to at most six explicit p-adic congruences. A further scalar reduction (Corollary 14. 2) collapses these to a single congruence: Aₚ^mix ≡ 18 (mod p⁴), equivalently S (p) ≡ 27 (mod p⁴) for a finite Lagrange–Bürmann sum of companion coefficients. The mod p closure (Theorem 14. 3) is proved unconditionally via Wolstenholme, Fermat, and the unit-root property of the companion sequence. The companion endpoint congruence Ã₏−₁ ≡ 2·27^p−1 − 1 (mod p²) is proved (Theorem 14. 4) using a six-step argument: dominant-term extraction from the triple Pochhammer sum, reflection symmetry of the Pochhammer product, a pairing argument for partial harmonic sums, Wolstenholme's theorem, and the Eisenstein–Lerch formula relating partial harmonic sums to the Fermat quotient of 3. The mod p² closure S (p) ≡ 27 (mod p²) follows unconditionally (Proposition 14. 5), with middle terms eliminated by a self-reciprocity pairing on the companion generating function. The first open obstruction is at the mod p³ level, where the middle terms of the Lagrange–Bürmann sum contribute. All results through mod p² — order drop, modular dictionary, split/inert dichotomy, module-wide failure, Hecke–Fricke finite reduction, scalar reduction, and the mod p² closure — are unconditional and self-contained.