Let $K_M \subset \mathbb{R}^3$ be the "snaky" corridor with unit-square cross-section: an infinite entry arm parallel to the $x$-axis, a middle arm parallel to the $y$-axis whose clear straight section has length $M$, and an infinite exit arm parallel to the $z$-axis, with the two turns lying in the $x$-$y$ and $y$-$z$ planes. Let $V^*(K_M)$ be the supremum of the volumes of connected bodies that can be moved continuously (by rigid motions) from the entry arm to the exit arm while remaining inside $K_M$. We prove $V^*(K_M) \le 7.8691$ for every $M \ge 3.53$ (Theorem A); by a sharper analysis of the same mechanism, $V^*(K_M) \le 4.2862$ for every $M \ge 2.61$ (Theorem B); and, by replacing the final analytic caps with a certified branch-and-bound computation over the compact family of entry tubes compatible with the forced events, $V^*(K_M) \le 3.4083$ for every $M > 2.2$ (Theorem C; computer-assisted, in double precision with conservative slack). In particular all three bounds apply to the corridor with $M = 4$ used in Problem 6.64 of Georgiev, Gómez-Serrano, Tao and Wagner (arXiv:2511.02864), and uniformly to every "turns far apart" reading of that problem. To the best of our knowledge, this is the first upper bound for the snaky-corridor 3D moving sofa problem; previously not even finiteness of $V^*$ had been recorded. This note proves upper bounds only; combined with the certified lower bound 1.8558404 from the author's separate certification work via the problem's own evaluation pipeline, the state of the problem becomes $1.8558404 \le V^*(K_4) \le 3.4083$. Theorems A and B are elementary and self-contained: a first-crossing (elbow) event forces a definite tilt of the body's own entry tube, and Fubini-type chord estimates for tilted tubes cap the volume. Theorem C certifies, by the same forced-event skeleton, the largest corridor volume that any admissible entry tube can carry.

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