Motion planning in clutter is embodiment-specific: the feasible free space and reachable commands depend on each robot's geometry and dynamics. Existing cross-embodiment policies output normalized commands that disregard these differences, or compensate through per-robot training and distillation. World models can in principle pool cross-embodiment data, yet command-conditioned models bind their latent dynamics to a single action space, while pose-conditioned models omit the mapping from commands to body-specific motion. On flat ground, however, embodiment affects the planner's observations only through the camera ego-motion. This letter proposes Hourglass, an hourglass-shaped architecture that factorizes cross-embodiment motion planning at this interface: a body-agnostic world model and each robot's differentiable ego-dynamics, which map commands to that ego-motion, are coupled only through it. The world model is trained on data pooled across embodiments and camera mounts; each robot's ego-dynamics is a reduced-order template with identified physical parameters. A generalist parameter-conditioned policy is learned once at this junction: each imagined step rolls out the template and then the world model, and imagination training through each robot's template makes the policy body-aware. On seven simulated robots of five locomotion types, the generalist policy outperforms imitation-learning and diffusion-policy baselines on the same world model by 3.8–10.6 percentage points in success rate and matches per-robot specialists without dedicated training, while approaching its parameter-conditioned MPPI teacher within 1.4–2.8 points without an online map. After three minutes of teleoperated driving for identification, the synthetic-data-trained model transfers zero-shot to a real skid-steer robot unseen in training, navigating unseen indoor scenes.